There are two parts.
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°. Find the height of the shorter building to the nearest meter
a. 13 m
b. 49 m
c. 190 m
d. 193 m
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.
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.
To find the height of the shorter building, we can use the tangent function:
tan(15°) = (207 - h)/51
where h is the height of the shorter building.
Solving for h, we get:
h = 207 - 51*tan(15°)
h ≈ 193 m
Therefore, the answer is d. 193 m.
For the second question, the angle of depression from the top of the taller building and the angle of elevation from the top of the shorter building are complementary angles. Therefore, the answer is b. They are complementary.