Two office buildings are 51 meters apart. The height of the taller building is 207 meters. 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
(1 point)
A. 13 m
B. 49 m
C.190 m
D.193 m
To solve this problem, we can use the trigonometric function tangent.
Let's denote the height of the shorter building as h. The angle of depression is the angle formed by looking downward from a vertical line, so the tangent of this angle can be represented as the ratio of the height of the shorter building to the horizontal distance between the two buildings:
tan(15) = h/51
To find h, we can multiply both sides of the equation by 51 and then take the tangent of 15:
h = 51 * tan(15)
Using a calculator, we find that tan(15) ≈ 0.268, so
h ≈ 51 * 0.268 ≈ 13.69
Therefore, the height of the shorter building is approximately 14 meters.
The correct answer is A. 13 m.