Question

The length of a shadow of a building is 10 m. The distance from the top of the building to the tip of the shadow is 26 m. Find the height of the building

Answer 1

The height of the building is 24m

Explanation:

This can be solved using the Pythagorean theorem

which states that the three sides of a right triangle are related by the equation

`c^2 = a^(2) + b^(2)` (see figure)

where c is the hypotenuse and a, b are the other two sides

Here we have c = the distance from the top of the building to the tip of the shadow = 26m

One side, the length of the shadow ie b = 10 m

So we have

`26^2 = a^2 + 10^2` where a is the height of the building

Switch sides to get

`a^2 + 10^2 = 26^2`

`a^2 + 100 = 676`

Subtract 100 from both sides

`a^2 = 676 - 100 = 576`

`a = √(576)`

a = 24

The height of the building is 24m