HELP ASAP From her bedroom window, Makala is 20ft. Away from a tree in her yard. The angle of elevation from her line of sight to the top of the tree is 42°. The angle of depression from her line of sight to the bottom of the tree is 31°. Find the height of the tree to nearest foot.​

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Explanation:

It might help to erase any unneeded stuff from the drawing. Refer to the diagram below to see what I mean. We have two triangles and we need to find the lengths of BD and DC, which are x and y respectively.

To find each of them, we'll use the tangent ratio since it connects the opposite and adjacent sides together.

Focus on triangle ADB up top

tan(angle) = opposite/adjacent

tan(A) = BD/AD

tan(42) = x/20

20*tan(42) = x

x = 20*tan(42)

x = 18.0080808859568 which is approximate.

x = 18.008

So the length of segment BD is roughly 18.008 feet.

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We'll use this same idea to find y. Focus on triangle ADC.

tan(angle) = opposite/adjacent

tan(A) = DC/AD

tan(31) = y/20

20*tan(31) = y

y = 20*tan(31)

y = 12.0172123805512 which is also approximate

y = 12.017

Segment DC is approximately 12.017 feet

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At the end of the each of the last two sections we found that

segment BD =  18.008 feet

segment DC = 12.017 feet

add those two segments together to get the length of segment BC, which is the height of the tree

BC = BD+DC

BC = 18.008 + 12.017

BC = 30.025

BC = 30 feet, which is the final answer

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If you wanted to calculate everything in nearly one step, then you could say

20*tan(42)+20*tan(31) = 30.02529 = 30

This one step calculation is simply a quick summary of what the last two sections are talking about in more step by step detail.