A peer is having difficulty finding angle measures using trigonometric ratios in a right triangle. Create an example to demonstrate how to do this and be sure to address using the reciprocal relationships (cosecant, secant, cotangent too)
Answers
A right triangle has 3 main trigonometric ratios. These ratios are the relationships between different sides of the triangle, how large one side is compared to the other side. If you have every angle, in degrees, of a triangle, then you can figure out the relation between the lengths of the three sides. Additionally, you can figure out the value of the angles, given the sides of the triangle.
In the diagram, we are interested in the trigonometric ratios with respect to angle a.
You see in the diagram that sine, cosine, and tangeant are described as their ratios: (one way to remember: SohCahToa
sine = opposite / hypotenuse
cosine = adjacent / hypotenuse
tangeant = opposite / adjacent.
cosecant, secant, and cotangents are just the reciprocals of these ratios:
cosecant = 1 / sin
secant = 1 / cosine
cotangeant = 1 / tangeant
Final answer:
To find angle measures using trigonometric ratios, such as sine, cosine, and tangent, as well as their reciprocals (cosecant, secant, and cotangent), use SOHCAHTOA to relate the sides of the triangle to the angle. Utilize the inverse trigonometric functions (like arccos) on your calculator to find the angle's measure from the ratio you have calculated with sides of the triangle.
Explanation:
To find angle measures using trigonometric ratios in a right triangle, we can use the mnemonic SOHCAHTOA, which stands for Sine equals Opposite over Hypotenuse, Cosine equals Adjacent over Hypotenuse, and Tangent equals Opposite over Adjacent. Let's create an example:
Suppose we have a right triangle with a hypotenuse (h) of 10 units and an adjacent side (x) to angle theta of 8 units.
To find the cosine of angle theta, we use the ratio Cos(theta) = x/h. Thus, Cos(theta) = 8/10 = 0.8.
To determine the actual measure of angle theta, we use the inverse cosine function: theta = arccos(0.8), which gives us the angle's measure in degrees or radians.
For the reciprocal, secant (Sec) is simply the inverse of cosine: Sec(theta) = 1/Cos(theta) = 10/8 = 1.25.
If we needed to use the cotangent, which is the reciprocal of the tangent, we would first need to find the opposite side (y) using the Pythagorean theorem and then use the ratio Cot(theta) = x/y.
It's essential to understand these relationships and how to use the inverse functions to find the angle measures in a right triangle. Reciprocal relationships involve the use of cosecant (Csc), which is 1/Sin(theta), secant (Sec), and cotangent (Cot), which is 1/Tan(theta). Always make sure your calculator is set to the correct unit (degrees or radians) before calculating the angle.
Related Questions
Jim has received scores of 72 72 and 77 77 on his first two 100 point tests. what score must he get on his third 100 point test to keep an average of 79 79 or greater?
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149/2=74.5
through the process of elimination, I found that Jim needs to get an 88 or higher to receive an average of 79 or greater.
77+72+88=237
237/3=79
a deck of 28 cards contains 6 blue cards, 13 red cards and, 9 yellow cards what is the probability of randomly drawing a blue card from this deck?
Answer choices:
1/6
1/3
11/14
3/14
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If 7 times a certain number is added to 12, the result is 47
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So we can write this out as an equation, or:
7x + 12 = 47
Now we can just solve this.
7x + 12 - 12 = 47 - 12
7x = 35
/7 /7
x = 5
So the certain number is 5.
what is the value for X?
- 24
-9
-21
-14
what is the measure of <1?
- 45
- 60
- 120
-125
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What is 2.828427125 to the nearest thousandth?
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How do I solve this?
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If 3x-1>=0 then
x>=1/3
|3x-1\=3x-1
2*|3x-1|=18
2*(3x-1)=18
6x-2=18
6x=20
x=10/3
else
x<1/3
|3x-1|=-(3x-1)
2*|3x-1|=18
2(-(3x-1))=18
-6x+2=18
-6x=16
x=-8/3
endif
Write a function rule: 7 more than the quotient of a number n and 4 is 9
pls help!!!
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Given that ΔJKL ≅ ΔUVW and ΔUVW ≅ ΔABC, complete the following statements. Triangle JKL is congruent to triangle ABCBCACBA. Side LK corresponds to sides UV and ABVU and BCWV and CB. Angle JLK corresponds to angles UVW and ABCUWV and ACBWUV and CAB
Answers
Triangle JKL is congruent to triangle ABC.
Side LK corresponds to sides WV and CB.
Angle JLK corresponds to angles UWV and ACB.
For ΔJKL ≅ ΔUVW and ΔUVW ≅ ΔABC, we conclude congruence JKL ≅ ABC, LK corresponds to UV and AB, and JLK corresponds to UVW and ABC.
The given information implies that triangle JKL is congruent to triangle ABC, and side LK corresponds to sides UV and AB. Angle JLK corresponds to angles UVW and ABC.
Therefore, the statements can be completed as follows:
Triangle JKL is congruent to triangle ABC.
Side LK corresponds to sides UV and AB.
Angle JLK corresponds to angles UVW and ABC.
Therefore, these statements reflect the congruence relationships established through the given information.
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Suppose you work for a large coffee distributor that has a secret coffee blend it sells to local stores. You mix the Mexican Shade Grown blend with the Rift Valley blend, but always in the same proportion. Yesterday, you mixed 80 pounds of the Mexican Shade Grown blend with 24 pounds of the Rift Valley blend. Today, there is 60 pounds of the Mexican Shade Grown coffee left in stock. How many pounds of the Rift Valley coffee should you mix with it to get your secret blend?
Answers
It's 18 pounds of Rift Valley.
To get the secret blend, you should mix 18 pounds of the Rift Valley coffee with the 60 pounds of Mexican Shade Grown coffee.
Explanation:To find out how many pounds of the Rift Valley blend you should mix with the 60 pounds of Mexican Shade Grown coffee, we need to set up a proportion based on the ratio of the two blends. The ratio of the Mexican Shade Grown blend to the Rift Valley blend is 80:24, which can be simplified to 10:3. We can then set up the proportion: 10/3 = 60/x. By cross-multiplying, we get 10x = 180. Dividing both sides by 10, we find that x = 18. Therefore, you should mix 18 pounds of the Rift Valley coffee with the 60 pounds of Mexican Shade Grown coffee to get your secret blend.
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Please help.
The graph of the function f(x)=|x+3| is translated 5 units down.
What is the equation of the transformed function?
Enter your answer in the box.
g(x)= _________
Answers
down five units means add -5 to then end of the equation
Keywords
transformed function, translation, rule
In this problem we have
[tex]f(x)=|x+3|[/tex]
we know that
If the translation is [tex]5[/tex] units down
then
the rule of the translation is equal to
[tex](x,y)-------> (x,y-5)[/tex]
therefore
the answer is
the equation of the transformed function is equal to
[tex]g(x)=|x+3|-5[/tex]
see the attached figure to better understand the problem
3 out of 5 picks are orange.If 12 picks are orange,how many picks are there in all?
Answers
If A = James's present age, write an expression for his age seven years from now.
Answers
Answer:
A + 7Step-by-step explanation:
Given,
James's present age be = A
So,
After seven years from now will be +7
Therefore,
James age, seven years after his present age is,
= (A) + (7)
= A + 7
Hence, the required expression is: A + 7 (Ans)
Hello there, I hope you are having a nice day.
We are given that James's present age is A years.
If James's present age is a years, then in 7 years his age will be
A+7
Which means that whatever A is, it will be 7 more in 7 years.
Hence, the expression is A+7 (Answer)
Hope it helps.
~An emotional teen who helps others and listens to her favourite song "How Far I'll Go"
-Grace ;-)
Good luck with your studies.
A student measures a rectangular room to be 20.0 m * 17.16m. which of the numbers below represents the room's area with the correct number of significant figures
Answers
A = L x W
in which A is the area, L is the length, and W is the width. Substituting the known values to the equation,
A = (20.0 m)(17.16 m) = 343.2 m²
Since, the least number of significant figures in the multiplier is 3, our answer ought to be in 3 significant figures. The answer to this item is therefore 343 m².
HELP PLEASE
Which of the following graphs is not a function
Answers
In this case, the heart is not a function, because if you cut it up-down direction, your imaginary knife will touch the edge of the heart twice.
I hope this explanation helps.
A grocery store sells crackers in three box sizes. Which size box is the best buy? 8 oz for $2.00 12 oz for $2.64 16 oz for $3.20
Answers
$ 2.64 / 12 = 0.22 and $ 3.20 / 16 = 0.2. So the correct answer would be, 8 oz for $2.00.
Answer:
Option C is the correct choice.
Step-by-step explanation:
We have been given that a grocery store sells crackers in three box sizes.
To find the best buy, we will find the cost of per ounce crackers for each box.
[tex]\text{The price per oz for option A}=\frac{\$2}{8\text{ oz}}[/tex]
[tex]\text{The price per oz for option A}=\frac{\$0.25}{\text{ oz}}[/tex]
Therefore, the option A offers $0.25 for per oz of crackers.
[tex]\text{The price per oz for option B}=\frac{\$2.64}{12\text{ oz}}[/tex]
[tex]\text{The price per oz for option B}=\frac{\$0.22}{\text{ oz}}[/tex]
Therefore, the option B offers $0.22 for per oz of crackers.
[tex]\text{The price per oz for option C}=\frac{\$3.20}{16\text{ oz}}[/tex]
[tex]\text{The price per oz for option C}=\frac{\$0.20}{\text{ oz}}[/tex]
Therefore, the option C offers $0.20 for per oz of crackers.
Since the price offered by option C is less than other two options, therefore, option C is the correct choice.
How did geography influence the economy in the Mid-Atlantic/Middle colonies?
A) Different land types allowed colonists to export crops and other goods.
B) The short growing season allowed colonists to grow many types of grains.
C) Poor soils and rocky hills caused colonists to import most of their grains.
D) The many natural resources available drove colonists to focus on agriculture.
Answers
A) Different land types allowed colonists to export crops and other goods.
∠A and ∠B are vertical angles with m∠A=x and m∠B=4x−30 . What is m∠A ? Enter your answer in the box.
Answers
Answer:
[tex] x = 4x -30[/tex]
We can solve for x subtracting x on both sides:
[tex] x-x= 4x-x-30[/tex]
And then we can add 30 in both sides:
[tex] 30= 3x[/tex]
And dividing both sides by 3 we got:
[tex] x = 10[/tex]
Step-by-step explanation:
For this case we know the measure of two angles:
[tex]m <A = x[/tex]
[tex] m<B = 4x-30[/tex]
And we know that both angles are vertical and by definition vertical angles are the angles opposite each other when two lines cross.
For this case since both angles are vertical we have the property that:
[tex] m<A = m<B [/tex]
And replacing what we got we have:
[tex] x = 4x -30[/tex]
We can solve for x subtracting x on both sides:
[tex] x-x= 4x-x-30[/tex]
And then we can add 30 in both sides:
[tex] 30= 3x[/tex]
And dividing both sides by 3 we got:
[tex] x = 10[/tex]
If a set of xy-axes has 20 grid units in each direction and the greatest value the data to be placed on the horizontal axis is 132, what would be the appropriate and convenient scale to use for this axis? Explain
Answers
Thus will make the graph spread adequately across the axis as well provide a good sub-units for the graph (i.e. each grid unit will be divided into 8 equal subunits)
which polygon does NOT belong with the other three?
A. parallelogram
B. rectangle
C. rhombus
D. Pentagon
Answers
Answer:
The polygon that does NOT belong with the other three is a pentagon.
Step-by-step explanation:
A polygon is a 2 D shape formed with straight lines. Like - triangles, quadrilaterals, pentagons, hexagons etc.
Here in the given choices, parallelogram , rectangle and rhombus all are four sided polygons and has parallel sides.
Only pentagon has 5 sides with no parallel sides.
Hence, the polygon that does NOT belong with the other three is a pentagon.
Change the column heading for the row sum column which represents the total of each type of session, to total number of sessions
Answers
You can change a column heading by clicking it, then right-clicking to select 'Rename Column' and inputting 'Total Number of Sessions'.
Explanation:To change the column heading for the row sum which represents the total of each type of session to 'Total Number of Sessions', you need to follow these steps:
Firstly, click on the column heading which you want to change. This will usually highlight the entire column.Right-click on the highlighted column heading, and select 'Rename Column' from the drop-down menu.In the text box that appears, type 'Total Number of Sessions' and hit 'Enter'.This will effectively rename your column heading to represent the total number of sessions accurately.
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ABC and CBD form a linear pair and have equal measures. Tell if ABC is acute, right, or obtuse
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but if they have equal measures....180/2 = 90...then they would both equal 90 degrees.....and 90 degrees is a right angle.
So ABC and CBD are both right angles
Answer:
Right angle
Step-by-step explanation:
When two lines intersect, a linear pair is formed, two angles being linear pair means the sum of those two angles is 180°.
Now if ∠ABC and ∠CBD for a linear pair,
∴∠ABC + ∠CBD = 180°
also given that ∠ABC and ∠CBD are of equal measure
∴ ∠ABC + ∠ABC = 180°
⇒ ∠ABC = 90° = ∠CBD
∴ ∠ABC is right angle
Which line segment is parallel to plane FGKJ?
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One theme from "The Yellow Wallpaper" is that women played a lesser role in marriage during the 19th century. Which line from the passage best supports this theme?
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Answer: Answer is A for apex ; ` And I know John would think it absurd. But I MUST say what I feel and think in some way - it is such a relief! ´
Step-by-step explanation:
The cost of a ticket to ride a roller coaster at the fair is $2. there are n people in a group who want to go on the ride. write an expression that describes the total amount of money the group will need to ride this roller coaster.
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n(2)
Can someone explain to me what a consistent-dependent system is?
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The average rate of change of the function between x = 15 to x = 29 is __________m/s2 and represents the car's acceleration.
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Answer:
sorry guys that other question is absolutely no help at all. The answer is 1.266 m/s squared. I don't know what kind of IDIOT would try and take you to a completely other website.
Step-by-step explanation:
81 1/4 is equal to 2. True or False
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81 1/4 is much greater than 2.
What is the original price of a telescope the discount is 30% and the sale price is $126?
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[tex]\displaystyle x\cdot \frac{30}{100} = 126 \\\\ \frac{3x}{10}=126\\\\3x=1260\\\\x=420 [/tex]
How do I solve this?
Answers
-c^2-4c+21
From here, we’ll factor out a -1 so that we have:
-(c^2+4c-21)
Let’s focus on the quadratic expression inside the parentheses. To find our factors (c + x)(c + y), we’ll need to find two terms x and y that multiply together to make -21 and add together to make 4. It turns out that the numbers -3 and 7 work out perfectly for that purpose (-3 x 7 = -21 and 7 + (-3) = 4), so substituting them in for x and y, we have:
(c + (-3))(c + 7)
(c - 3)(c + 7)
And adding back on the negative from a few steps earlier:
-(c - 3)(c + 7)
From a point level with and 1000ft away from the base of the washington monument, the angle of elevation to the top of the momument is 29 degrees. find the height of the monument