Question

Answer Quickly Please! Two office buildings are 51 m apart. The height of the taller building is 207 m. The angle of depression from the top of the taller building to the top of the shorter building is 15 degrees. Find the height of the shorter building to the nearest meter.

13m
49m
190m
193m
In the previous question, how does the angle of depression from the top of the taller building relate to the angle of elevation from the top of the shorter building? Choose all that apply.(Hint: Two correct answer choices)
A. They are congruent
B. They are complementary
C. They are supplementary
D. They are alternate interior angles
E. They are alternate exterior angles
F. They are corresponding angles
Thank you!

Answer 1

To the first question it should be:
193 meters tall

Answer 2

Part 1: 193.33 meters

Part 2: A and D

Explanation:

We are given that,

Height of the taller building 'A' = 207 meter

Distance between both the buildings = 51 meter

Angle of depression from the top of the taller building to the top of the smaller building = 15°

Since, we know that, 'The angle of depression is equal to the angle of elevation'

We get the figure below for the situation.

Part 1: To find the height of the smaller building.

Using trigonometric form for the angles in right triangles, we get,

`\tan 15=(x)/(51)`

i.e.
`x=51* \tan 15`

i.e.
`x=51* 0.268`

i.e. x= 13.67 meters.

So, the height of the smaller building 'y' = 207 - 13.67 = 193.33 meters

Hence, the height of the smaller building is 193.33 meters

Part 2: Relation between the angle of depression and the angle of elevation.

Since, both the angles are made when a transversal intersects two parallel lines.

And, 'when the transversal intersects two parallel lines, the alternate interior angles are same'.

So, we have that, the correct options for the angle of depression and the angle of elevation are:

A. They are congruent

D. They are alternate interior angles.