The angle of elevation of the top of a building from a point Z on the ground is 50°. If the height of the…

Analyze the question

A building is 124 m tall. From point Z on the ground, the angle of elevation to the top is 50°. We need the horizontal distance from Z to the foot of the building.

Concept

This is a right-angled triangle problem:

• Opposite side = height of building = 124 m
• Adjacent side = distance from Z to the foot = d
• Angle = 50°

The ratio that links opposite and adjacent is tangent:

tan θ = opposite / adjacent

Solution

tan 50° = 124 / d

d = 124 / tan 50°

tan 50° ≈ 1.1918

d = 124 / 1.1918 ≈ 104.05 m

Answer

The distance is about 104.05 m, which is option B.

Tip

Remember SOH-CAH-TOA. When a question gives the height (opposite) and asks for the distance along the ground (adjacent), use TOA. Also, when you divide by tan of an angle larger than 45°, the answer will be smaller than the height, since tan 50° > 1. Here 104.05 < 124, which is a quick check that your answer is sensible.