Find the height of a building which casts a 30meter horizontal shadow when the angle of elevation of the sun is 60°.

Answer 1

The angle is 60 degrees is θ. The shadow is 30 meters is adjacent to that angle. The height of the building is opposite of that angle.

tangent(θ) = opposite / adjacent

tangent(60) = height / 30

30 * tangent(60) = height

You can calculate tangent(60) using a calculator set to degrees or by dividing (√3 / 2) by (1 / 2) from the unit circle. This just equals √3 or about 1.732

So the height of the building is 30 * √3 ≈ 30 * 1.732 ≈ 51.962 meters.

If you need help with the unit circle and basic trig, please book a lesson with me and I will show you the way in greater detail.