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March 25th, 2017, 01:37 AM   #1
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Trigonometry- Angle of elevation, depression

A man is looking out of his apartment window at the office building across the street. From the man’s point of view, the angle of elevation to the top of the office building is 57.5 degrees , while the angle of depression to the base of the office building is 41.2 degrees . Find:
a. the altitude of the man’s eyes AND the height of the office building if the apartment and the office building are 14.6 meters apart
b. the altitude of the man’s eyes AND the distance between the office building and the apartment if the height of the office building is 41.8 meters

How would I solve this question?? I don't understand this question at all...

Pls help!

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Kirtana Devaraj is offline  
 
March 25th, 2017, 05:57 AM   #2
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Have you drawn a diagram (two actually one for each part of the question)?

Angles of elevation and depression are measured from the horizontal.
So this gives you two right angled triangles in each case with the angle of elevation or depression providing another angle and that part of the question one of the sides so you can calculate the other side by trigonometry.

What else did you not understand?
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March 25th, 2017, 06:03 AM   #3
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Quote:
Originally Posted by Kirtana Devaraj View Post
A man is looking out of his apartment window at the office building across the street. From the man’s point of view, the angle of elevation to the top of the office building is 57.5 degrees , while the angle of depression to the base of the office building is 41.2 degrees . Find:
a. the altitude of the man’s eyes AND the height of the office building if the apartment and the office building are 14.6 meters apart
b. the altitude of the man’s eyes AND the distance between the office building and the apartment if the height of the office building is 41.8 meters
first step is to make a sketch of the problem (attached)

$\color{red}{y}$ = height of the man's eye above the ground

$\color{red}{H-y}$ = height of the building

$\color{red}{x}$ = horizontal distance between the buildings

two equations ...

$\tan(57.5) = \dfrac{H-y}{x}$

$\tan(41.2) = \dfrac{y}{x}$

for part (a), you are given $x = 14.6 \, m$, solve for $H \text{ and } y$

for part (b), you are given $H = 41.8 \, m$, solve for $x \text{ and } y$
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