Question

Two buildings are 30 m apart. The angle from the top of the shorter building to the top of the taller building is. The angle from the top of the shorter building to the base of the taller building is. What is the height of the taller building?

Answer 1

The height of the taller building is: 51.345m

Explanation:

Given

The question has missing details (See attachment for the illustration of the complete question)

Required

The height of the tall building

The height, a, is calculated as:

`a = b +c`

To solve for b, we consider the upper half of the attached image

The upper half is a right triangle.

Using tan formula, we have:

`tan(31) = (b)/(30)`

Solve for b

`b = 30 * tan(31)`

To solve for c, we consider the lower half of the attached image

Using tan formula, we have:

`tan(48) = (c)/(30)`

Solve for c

`c = 30 * tan(48)`

Recall that:
`a = b +c`

So:

`a = 30 * tan(31) + 30 * tan(48)`

`a = 30 * 0.6009 + 30 * 1.1106`

`a = 18.027 + 33.318`

`a = 51.345`