Question

From the top of a 200 meters high building, the angle of depression to the bottom of a second building is 20 degrees. From the same point, the angle of elevation to the top of the second building is 10 degrees. Calculate the height of the second building to the nearest hundred meters.

Answer 1

Let's call the height of the second building "x". We can use trigonometry to solve for x.

First, let's draw a diagram to help visualize the problem:

A B

\ /

\ /

\ / x

\/

C

Where:

A is the top of the 200 meters high building

B is the bottom of the second building

C is the point from which the angles of depression and elevation are measured

x is the height of the second building

From the diagram, we can see that:

angle BCA = 20 degrees (angle of depression)

angle BAC = 10 degrees (angle of elevation)

AB = 200 meters

Using the tangent function, we can write:

tan(20) = x / AB (tangent of angle BCA)

tan(10) = x / (AB + x) (tangent of angle BAC)

We can solve these equations for x:

x = AB * tan(20) (multiply both sides by AB)

x = (AB * tan(10)) / (1 - tan(10)) (multiply both sides by 1 - tan(10), then simplify)

Plugging in the values we know:

x = 200 * tan(20)

x = (200 * tan(10)) / (1 - tan(10))

Using a calculator:

x ≈ 67.35 meters

Therefore, the height of the second building is approximately 67 meters (to the nearest hundred meters).