Joel is walking down a street and sees a 115 ft tall building in front of him. he stops 190 feet from the base of the building at the tip of the building's shadow. round answers to three decimal places.
a. if there was a piece of rope from the top of the building to joel, how long would it be?
b. what is the angle of elevation from joel to the top of the building?
c. margaret says that she could find the angle of depression from the top of the building to joel by subtracting the angle of elevation from 90°. is she correct? explain.
Answers
a) a²+b²=c²
(115)²+(190)²=c²
√49325=c
222.092 ft =c
b) tanθ= opp/adj
tanθ=115/190
θ=tan⁻¹(115/190)
θ=31.184 degrees
c) Yes, because the angle of depression and angle of elevation, in this case at least, add up to 90 degrees. Due to this, subtracting the angle of elevation by 90 degrees will give angle of depression.
Hope I helped :)
If there was a piece of rope from the top of the building to Joel, how long would it be approx 222.01 feet. The angle of elevation from Joel to the top of the building is approx [tex]31.18 ^ \circ[/tex]
What is angle of elevation and angle of depression?You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.
Similarly, there is angle of depression, when you look horizontal, then down, the angle between both positions is the angle of depression.
How to use right triangles to find the length of the rope?Remember that we assume that buildings are usually vertical to the ground. This means, there is 90° formation. The length of the rope can be taken as length of hypotenuse.
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Referring to the figure attached below, we get:
Length of the rope = Length of the line segment AC = |AC|
Using the fact that the triangle ABC is right angled triangle, we can use Pythagoras theorem.
We get the length of AC as:
[tex]|AC|^2 = |AB|^2 + |BC|^2\\|AC| = \sqrt{|AB|^2 + |BC|^2} \\\text{positive square root since length is non-negative quantity}\\\\|AC| = \sqrt{115^2 + 190^2} = \sqrt{51325} \approx 222.01 \: \rm ft[/tex]
Thus, if there was a piece of rope from the top of the building to Joel, how long would it be approx 222.01 feet.
The angle of elevation is calculated as:
[tex]\tan(\angle ABC) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}} = \dfrac{|AB|}{|BC|}\\\theta = tan^{-1}(\dfrac{115}{190}) \approx 31.18^\circ[/tex]
The angle of depression is actually equal to angle of depression because they are pair of alternate interior angles (made by traversing line AC between two parallel lines).
Thus, Margaret statement is false.
Therefore, we get the answers as:
If there was a piece of rope from the top of the building to Joel, how long would it be approx 222.01 feet.The angle of elevation from Joel to the top of the building is approx [tex]31.18 ^ \circ[/tex]Margaret's statement is false.Learn more about Pythagoras theorem here:
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hope that helps, God bless!
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Answer:
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