Question

a surveyor 85 feet away from a building measures the angle from the ground to the top of the building to be 48°. what is the height of the building? ? feet round your answer to the nearest hundredth.

Explanation:

Step1: Set up tangent - ratio

We know that in a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Let the height of the building be $h$. The distance from the surveyor to the building is the adjacent side ($85$ feet) and the height of the building is the opposite side. The angle of elevation $\theta = 48^{\circ}$. So, $\tan(48^{\circ})=\frac{h}{85}$.

Step2: Solve for $h$

Multiply both sides of the equation by $85$: $h = 85\times\tan(48^{\circ})$.
We know that $\tan(48^{\circ})\approx1.1106125149$. Then $h = 85\times1.1106125149\approx94.40206377$.
Rounding to the nearest hundredth, $h\approx94.40$.

Answer:

$94.40$