Question

After walking 300 m away from the base of a tall building on level ground, Elise measured the angle of elevation to the top of the building to be 54°. Find the height of the building to the nearest metre.

Answer 1

413 meters

Explanation:

Elise's observation forms a right triangle with the base of the building, the top of the building, and her position. The height of the building is the opposite side to the angle she measured, and her walking distance is the adjacent side. We can use the tangent of the measured angle to find the height of the building.

Tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. So, we have:

tan(angle) = opposite/adjacent

We can rearrange this to solve for the opposite side, which is the height of the building:

opposite = tan(angle) * adjacent

Substituting the given values:

opposite = tan(54°) * 300 m

To find the height of the building, we need to calculate the tangent of 54 degrees and multiply it by 300. The tangent of 54 degrees is approximately 1.376381920471173.

So let's calculate:

Height = tan(54°) * 300 m ≈ 1.376381920471173 * 300 m ≈ 412.91 m

Therefore, the height of the building is approximately 413 meters, to the nearest meter.