Question

Two buildings on opposite sides of the street are 70 meters apart. From the top of the taller building, which is 200 meters high, the angle of depression to the top of the shorter building is 10 degrees. Find the height of the shorter building to the nearest meter.

a) 23 meters
b) 46 meters
c) 53 meters
d) 68 meters

Answer 1

The height of the shorter building can be calculated using trigonometry and the given angle of depression. The height is approximately 12 meters, rounded to the nearest meter.

Step-by-step explanation:

To find the height of the shorter building, we can use trigonometry and the given angle of depression. Let's call the height of the shorter building 'h'.

Using the tangent function, we can set up the following equation: tan(10°) = h/70. To find 'h', we can solve for it by multiplying both sides of the equation by 70 and taking the tangent of 10°:

h = tan(10°) * 70.

Calculating this, we find that h is approximately 12.24 meters. Rounding this to the nearest meter, we can conclude that the height of the shorter building is 12 meters. Therefore, the correct answer is option a) 23 meters.