Question

Please help! There are only 3 choices.

Find the height of the tree in feet if the angle of depression is 31 degrees.
A) 7.2 feet
B) 10.3 feet
C) 6.2 feet

Answer 1

Answer: A) 7.2 feet

The value is approximate.

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Step-by-step explanation:

Check out the diagram below.

The angle of depression being 31 degrees refers to the idea of looking straight horizontal, then looking down 31 degrees. I recommend adding a dashed horizontal line.

That horizontal line is parallel to the ground. This forms a pair of congruent alternate interior angles. Therefore, we have two angles that are 31 degrees as the diagram shows.

The 31 degrees at the bottom is the angle of elevation.

Use this angle of elevation to say...

tan(angle) = opposite/adjacent

tan(31) = x/12

x = 12*tan(31)

x = 7.210327 approximately

This rounds to 7.2 feet

Answer 2

The answer is A 7.2 feet

This is because the first angle is 31
That means the other angle is 59 degrees
This means you can solve the rest of the triangle accordingly:)