Question

Standing 140 meters from a building, a surveyor measures the angle from the ground to the balcony as

13° How high is the balcony? Give your answer to the nearest tenth.

Answer 1

32.3 meters

Explanation:

We can model the given scenario as a right triangle, where the base of the triangle is the distance the surveyor is standing from the building (140 m) and the angle from the ground to the balcony is the angle of elevation (13°).

We want to find the height of the balcony, which is the height of the triangle.

As we have the side adjacent to the angle, and wish to find the side opposite the angle, we can use the tangent trigonometric ratio.

`\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=(O)/(A)$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}`

Given values:

• θ = 13°
• O = h
• A = 140

Substitute the values into the tan ratio and solve for h.

`\tan 13^(\circ)= (h)/(140)`

`140\tan 13^(\circ)=h`

`h=140\tan 13^(\circ)`

`h=32.3215467...`

`h=32.3\; \sf m\; (nearest\;tenth)`

Therefore, the height of the balcony is 32.3 meters, to the nearest tenth.