Mathematics High School

Two hikers on opposite sides of a canyon each stand precisely 525 meters above the canyon floor. they each sight a landmark on the canyon floor on a line directly between them. the angles of depression from each hiker to the landmark meter are 37° and 21°. how far apart are the hikers? round your answer to the nearest whole meter.

Answers

Answer 1

The hikers are 2064 m apart

The situation forms two right angle triangle.

Right angle triangle:

A right angle triangle has one of its sides as 90 degree.

Therefore,

First hiker distance

tan 37 = opposite / adjacent

tan 37° = 525 / x

x = 525 / tan 37

x = 696.711059326

x = 696. 711 m

Second Hiker distance:

tan 21 = 525 / y

y = 525 / tan 21

y = 1367.68613557

y = 1367.686 m

Distance apart = 696.711 + 1367.686 = 2064.39713557 = 2064 m

learn more on angles of depression here: https://brainly.com/question/10207139

Related Questions

The pressure P exerted by a force varies inversely as the area A on which the force is applied. If 16 N/ft2 of pressure is exerted by a force on an area of 3 ft2 , what is the pressure exerted by the same force on an area of 6 ft2?
A) 8 N/ft2
B) 16 N/ft2
C) 4 N/ft2
D) 32 N/ft2

Answers

The first piece of information tells you that
16 = C / 3
Solve for C
C=16×3=48
Now find P if A = 6. and C=48
P = C/6
P = 48/6
P = 8 N/ft2

Answer:

A) 8 N/ft2

Step-by-step explanation:

Pressure is the normal force per unit area, that is, it is equivalent to the force acting on the surface unit, and is given by:

[tex]P=\frac{F}{A}[/tex]

Where:

[tex]P=Pressure\\F=Normal\hspace{3}force\\A=Area\hspace{3} where \hspace{3}force\hspace{3} is \hspace{3}applied.[/tex]

In the first case:

[tex]P=16N/ft^2\\A=3ft^2[/tex]

Using the previous equation and solving for [tex]F[/tex] :

[tex]F=P*A=16*3=48N[/tex]

Now, for the second case, since the force is the same applied in the first case, then:

[tex]P=\frac{F}{A} =\frac{48}{6} =8N/ft^2[/tex]

Therefore the answer is:

A) 8 N/ft2

The janitor found that it was leaking at a rate of 13 fl oz per minute How fast was the pipe leaking in gallons per hour​?

Answers

8oz=1cup
16cup=1gal
so

16*8=128oz per gallon


13oz/min

alrighty
13oz=13/128gal
1min=1/60hr

(13/128gal)/(1/60hr)=(13/128gal)(60hr/1)=78hr/128gal
128gal/78hr=64gal/39hr≈6.09375
about 6 gallons per hour
the answer is 6 gallons per hour

Choose the correct description of the graph of the compound inequality

2x + 5 > 9 and 5x less than or equal to 30.

A) A number line with an open circle on 2, shading to the left, and a closed circle on 6, shading to the right
B) A number line with an open circle on 2, a closed circle on 6, and shading in between
C) A number line with a closed circle on 2, shading to the left, and an open circle on 6, shading to the right
D) A number line with a closed circle on 2, an open circle on 6, and shading in between

Answers

To do this, you first have to solve the first inequality for x: 2x+5>9, 2x>4 and x>2.  Now solve the next one for x as well: 5x <=30, x<=6.  Now work on putting them onto a number line together.  Since there is not an "equal to" with that greater than, the circle is open above the 2.  The next one has an "equal to" with it so that's a closed circle above the 6.  This is a conjunction, meaning the solution will show what is shared between the 2 inequalities, so you have an open circle above the 2 and shading to the right til you get to the closed circle above the 6 (which is technically shaded to the left down to the open circle at 2). So your choice is B.

Answer:

B) A number line with an open circle on 2, a closed circle on 6, and shading in between

Step-by-step explanation:

easy answer

Gabriella said a triangle with an angle of 98 degrees was an obtuse angle. Cynthia said a triangle with an angle of 98 degrees was an acute triangle. Who is right and why?

Answers

an obtuse triangle has an angle that is greater than 90 degrees

so if we see gabby's statement, ,98>90 so tecnically, she is correct

cynthya's statement is false because 98>90 so it is an obtuse angle

. If ON = 4x – 6, LM = 3x + 5, NM = x – 4, and OL = 4y – 3, find the values of x and y for which LMNO must be a parallelogram.

Answers

In a parallelogram, opposite sides are congruent.

This means that
LM = ON
NM = OL

Using the equations, find x and y:
4x - 6 = 3x + 5
4x = 3x + 11
1x = 11
x = 11

x - 4 = 4y - 3
x - 1 = 4y
-1 = 3y
-1/3 = y

The values are:
x = 11
y = -1/3

A line with a slope of 3 passes through the point (2,5) what is the equation of this line?

Answers

y=3x-4 because the form of a line's equation is y=mx+b where m is the slope or three in this case and b is the value of y in the y intercept and in this case it is -4 so you get y=3x+(-4) or y=3x-4.
Slope of the line equals 3 at the points (2,5) so m=0
The equation is a horizontal line, therefore the slope is 0.

Use 1% or 10% to estimate 8% of 310

Answers

We can obtain 8% of a value by finding the 10% of the value and subtract 2% of the value

10% of 310 = 310÷10 = 31
1% of 310 = 310÷100 = 3.1
2% of 310 = 2×3.1 = 6.2

8% of 310 = 31 - 6.2 = 24.8

write the ordered pair that represents yz. then find the magnitude of yz. Y(-5,7), Z(-1,2)

Answers

The order pair that represents yz can be found as follows:
yz = z - y = (-1 , 2) - (-5,7) = (4 , -5)

The magnitude of yz can be calculated as follows:
magnitude yz = sqrt [(4)^2 + (-5)^2]
                      = sqrt (41)
                      = 6.403

Answer: the answer is D on edge

Step-by-step explanation:

Can someone help me plz!!!

Answers

It is B. Identity always includes 0
you basically just say if it does equal to a+c and then say if its right or wrong

express 3/4, 7/16,and 5/8 with the LCD

Answers

The LCD (lowest common denominator) is the lowest common denominator of two or more fractions.

4 = 2²
16 = 2⁴
8 = 2³

Take common and non-common factors with highest exponent.

So LCD = 16

The new dneominator of all fractions is 16. Divide this number for the original denominators and multiply for numerator...

16/4 = 4
4*3 = 12

3/4 = 12/16

16/16 = 1
1*7 = 7

7/16 = 7/16

16/8 = 2
2*5 = 10

5/8 = 10/16

Find the measure of each exterior angle of a regular polygon with 24 sides

Answers

the measure of each interior angle would be 165 degrees

The formula for finding the measure of each exterior angle of a regular polygon is similar to the formula for finding the measure of each interior angle. We take the sum of the measures of the exterior angles which is always 360 degrees and we divide this by the number of sides in the polygon which is n. So the formula for finding the measure of each exterior angle of a regular polygon is simply 360 over n. In this problem since the polygon has 24 sides, we simply plug a 24 in for n and we have 360 over 15. 360 divided by 24 is 15. Therefore, the measure of each exterior angle of a regular polygon that has 24 sides is 15 degrees.

Someone pls help!? I don't get it

Answers

= x^(16/5)  
= x^(3 1/5)
= x^3  * x^1/5

= x^3   * fifthroot of x

Its the first choice

([solve by writing an equation])
A pair of jeans costs 75% as much as a pair of corduroy pants. what is the cost of each if the total cost for the jeans and cords is $42?
I know the answer is Jeans: $18 and Cords: $24 but how do I write that in an equation to solve??
thank you!!!

Answers

Let the pair of jeans cost x dollars and the pair of corduroy cost y dollars.

"A pair of jeans costs 75% as much as a pair of corduroy pants."

this means [tex] x=\frac{75}{100}*y [/tex], simplifying by 25:

[tex]x= \frac{3}{4} y[/tex]           (equation 1)


"the total cost for the jeans and cords is $42?"

x+y=42    (equation 2)

substitute x form equation 1, in equation 2

x+y=42 

[tex] \frac{3}{4} y+y=42[/tex]

[tex] \frac{3}{4} y+ \frac{4}{4} y=42[/tex]

[tex]7y=4*42 [/tex]

y=4*6=24

substitute y=24 in either of equations 1 or 2:

x+y=42    (equation 2)
x+24=42
x=42-24=18

Answer: Jeans cost 18$, Cords cost 24$ 

Help me with this please!!!

Answers

do a ratio

11/2=X/24

24*11 = 264

264/2 = 132

X= 132

 so 132 students

What is the length of a square

Answers

That would depend on how big or small the square is. 

what is f^-1(1)? inverse function

Answers

f(x) = y = x
f⁻¹(x) = x = y
If x = 1 → f(1) = y =1
if x = 1 → f⁻¹(1) = x = 1



A football team loses 3 yards on one play and 6 yards on another play. Write a sum of negative intergers to represent this situation. Find the sum and explain how it is related to the problem.

Answers

'loses three yards' as negative expression is -3
'loses six yards' as negative expression is -6

The negative sum is: [-3 + -6] and working this sum we get -9

This means the football team loses 9 yards altogether

Bilal is sharing candy with 6 of his friends. He has 5 over 6 of a bag of candy left after he takes what he wants. What fraction of candy will each of his friends get if he shares equally with them?

_____ of the bag









Jenny and Hanan are collecting clothes for a clothing drive. Hanan collected 1 half as many bags of clothes as Jenny did. If Jenny collected 3 over 4 of a bag of clothes, what portion of a bag of clothes did Hanan collect?

_____bags

Answers

5/36 bags.

the 2nd one is 3/8 bags

According to the empirical rule, for a distribution that is symmetrical and bell-shaped (in particular, for a normal distribution) approximately how much of the data values will lie within two standard deviations on each side of the mean?

Answers

A sketch of the normal distribution is shown in the figure below.
The mean is μ, and the curve is symmetric about the mean.
The total area under the curve is 1.

The standard deviation is σ.
The interval (μ-σ, μ+σ) contains approximately 68% of the total area.
The interval (μ-2σ, μ+2σ) contains approximately 95% of the total area.

Answer: 95%

Divide (x^5+15x^4+54x^3-25x^2-75x-42) by x+8

Please show all work

Answers

We want to evaluate
(x⁵ + 15x⁴ + 54x³ - 25x² - 75x - 42)/(x+8)

There are two ways to do it: (a) long division, and (b) synthetic division.

Long Division
                    x⁴ +  7x³  - 2x² - 9x - 3
       -------------------------------------------------
x+8 | x⁵ + 15x⁴ + 54x³ - 25x² - 75x - 42
         x⁵ +  8x⁴
        ------------------------------------------------
                  7x⁴ + 54x³ - 25x² - 75x - 42
                  7x⁴ + 56x³
                  ---------------------------------------
                         - 2x³  - 25x² - 75x - 42
                         - 2x³  - 16x²
                          ---------------------------------
                                    -  9x² - 75x - 42
                                    -  9x² - 72x
                                 ----------------------------
                                              -  3x - 42
                                              -  3x - 24
                                             -----------------
                                                        - 18

Answer: 
x⁴ + 7x³ - 2x² - 9x - 3 - 18/(x+8)

Synthetic Division

    --------------------------------------
-8 | 1  15  54  -25  -75  -42
         -8 -56    16    72   24
    -----------------------------------
      1   7   -2    -9     -3   -18

Answer:
x⁴ + 7x³ - 2x² - 9x - 3 - 18/(x+8)

A surveyor measures the angle of elevation to a point on a mountain to be 18 degrees the point on the mountain is horizontally 4 miles away from the surveyor the vertical change in elevation from the point where the surveyor is standing to the point on the mountain is___ miles?

Answers

This is right triangle trig and you are looking for the height of the triangle. The reference angle is 18 degrees, the side adjacent to that angle is 4 and you are looking for the side opposite the reference angle.  The trig identity that helps us find that missing side is tangent:
[tex]tan(18)= \frac{x}{4} [/tex]
and 4 tan(18) = x.
x = 1.3 miles

Answer:

1.3 miles

Step-by-step explanation:

Solution:-

- The surveyor stands at a platform that is B = 4 miles and at an elevation of θ = 18 ° away from the point on the mountain.

- We can construct a right triangle from surveyor to the point of observation. To determine the change in height/elevation (H) we will apply the trigonometric relation as follows:

                              tan ( θ ) = H / B

- Solve for the elevation (H):

                              H = B*tan ( θ )

                              H = 4*tan ( 18 )

                              H = 1.3 miles

- The change in elevation from surveyor to point of observation is H = 1.3 miles.

What is the taxi distance between A(2, 5) and B(7, 9)?

Answers

If by "taxi distance" you mean travelling along the sides of the right triangle created by the two points.

t=|x2-x1|+|y2-y1|

t=5+4

t=9 units

If you mean the actual distance between the two points then:

d^2=(x2-x1)^2+(y2-y1)^2

d^2=(7-2)^2+(9-5)^2

d^2=25+16

d^2=41

d=√41 units

d≈6.4 units (to nearest tenth of a unit)

PLZ I NEED HELP ASAP

Annie has a compost pile that produces 12 pounds of compost a day from yard waste. Which function expresses the amount of compost (c) as a function of the number of days (d)? The function representing the relationship between the amount of compost and the number of days is__, with the input as__.

Answers

If it produces 12 pounds each day, for any number of days, we can just multiply by 12, correct?? So that means c=12d. Remember your input will be the days since you have to put that in the equation to calculate how much compost you have. 

Answer: number of days: c=f(d) =12d

Imput:12

Step-by-step explanation:

Given tan A = .78 find angle A in degrees. Round your answer to the nearest hundredth.

Answers

Tangent is one of the simplest trigonometric functions which relates the sides of the triangle. This function is the ratio between the measure of the side opposite to the angle and the side adjacent to it. This can be calculated through the reverse equation of,
             tan⁻¹(0.78) = A
The value of A in the equation to the nearest hundredth is 37.95°. 

Answer:

[tex]A\approx 37.95^{\circ}[/tex]

Step-by-step explanation:

We have been given that [tex]\text{tan}(A)=0.78[/tex]. We are asked to find measure of angle A in degrees.

We will inverse tangent to find measure of angle A as:

[tex]A=\text{tan}^{-1}(0.78)[/tex]

[tex]A=37.954230875133^{\circ}[/tex]

Upon rounding our answer to nearest hundredth, we will get:

[tex]A\approx 37.95^{\circ}[/tex]

Therefore, the measure of angle A is approximately 37.95 degrees.

WILL GIVE BRAINLIEST PLEASE PLEASE PLEASE HELP ASAP!!

If <1 and <2 form a linear pair, m<1 = 100 + 20x, and m<2 = 20x, find
m<1 .

a.
2°
b.
40°
c.
140°
d.
180°

Answers

C is correct! i had the same exact test but in flvs
a linear pair means the two angles add up to equal 180 degrees
so
m<1 + m<2 = 180
 100 + 20x + 20x = 180
40x = 80
x = 2

m<1 = 100 + 20x  = 100 + 20(2) = 140

answer
c.
140°

The original value of the car is $18,000 and it depreciates by 50% each year what is the value of the car after three years

Answers

value = 18000*(1-0.50)^3 = 2250

value after 3 years = $2250

The formula is
A=p (1-r)^t
A the value of the car after 3 years?
P current value 18000
R rate of depreciation 0.5
T time 3years
A=18,000×(1−0.5)^(3)
A=2,250

Some facts about powers of ten are shown.

Use what you know about powers of ten to enter numbers that make the equation true.

Enter numbers to write 7.9×10^-6 in standard notation.

Answers

[tex]7.9*10^{-6}=7.9* \frac{1}{1,000,000}=0.0000079 [/tex]

The number to write [tex]7.9\times 10^-6[/tex] in standard notation is 0.0000079.

Given that,

The number to write the given equation in standard notation.

Based on the above information, the calculation is as follows:

[tex]= 7.9\times 10^-6 = 7.9 \times \frac{1}{1,000,000}[/tex]

= 0.0000079

Therefore we can conclude that the number to write [tex]7.9\times 10^-6[/tex] in standard notation is 0.0000079.

Learn more: brainly.com/question/7508826

What is the radius of the circle defined by x^2+2x+y^2+6y-39=0?

Answers

hello : 
x²+2x+y²+6y-39=0
(x²+2x+1)-1 +(y² +6y+9)-9 -39 =0
(x+1)² + (y+3)² = 49 = 7²
the radius is : 7

There are 50 jelly beans. if 7 of them are red, and 23 are black, what percentage of the jelly beans are not reed

Answers

86% bc 50 is easy to work with, you know 43 arent red, and since 43x2=86 its 86, multiply by 2 bc 50 is half of 100

In a circle with an 8-inch radius, a central angle has a measure of 60°. How long is the segment joining the endpoints of the arc cut off by the angle?


Answers

calculate circumference first:

C = 2πr
C = 2(3.14159)(8 inches)
C = 50.265 inches 

 then 60/360 = 1/6 of the circle 

  50.265 inches / 6
= 8.378 inches (Round answer as needed) 

Answer:

The length of segment joining the endpoints of the arc is [tex]8\ in[/tex]

Step-by-step explanation:

we know that

In the triangle ABC

see the attached figure to better understand the problem

[tex]AC=BC[/tex] -----> is the radius of the circle  

[tex]m<CAB=m<CBA[/tex]

[tex]m<ACB=60\°[/tex] ----> given problem (central angle)

Initially the triangle ABC is an isosceles triangle

Remember that

the sum of the internal angles of triangle must be equal to [tex]180\°[/tex]

For this particular case, the isosceles triangle ABC becomes an equilateral triangle, as the three angles are equal to [tex]60\°[/tex]

The equilateral triangle has three equal sides and tree equal angles

so

[tex]AC=BC=AB[/tex]

Hence

The length of segment joining the endpoints of the arc is [tex]8\ in[/tex]



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