Question

A 34 m building Casts a shadow. The distance from the top of the building to the tip of the shadow is 36 m find the length for the shadow if necessary around your answer to the nearest tenth

Answer 1

The shadow of the building reaches the ground and forms with the ground and the building itself a right triangle, i.e., a triangle with an angle of 90°.

In right triangles, the Pythagora's Theorem is satisfied.

If a and b are the shorter legs of a right triangle, and c is the length of the longer side (the hypotenuse), then:

`a^2+b^2=c^2`

Let's call a to the height of the building, b to the length of the shadow (the horizontal distance from the base of the building to the tip of the shadow), and c to the total length of the shadow from the top of the building right to the ground.

We need to find the value of b. Solving for b:

`b=\sqrt[]{c^2-a^2}`