Question

problem #3: a building is 50 ft high. at a distance away from the building, a person notices that the angle of elevation with the ground to the top of the building is 41°. how far is the person from the base of the building?

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the height of the building (opposite side to the angle of elevation) is 50 ft, the angle of elevation is \(41^\circ\), and we need to find the adjacent side (distance from the person to the building), let's call it \(x\). We use the tangent function, which is \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan(41^\circ)=\frac{50}{x}\).

Step2: Solve for \(x\)

Rearrange the formula to solve for \(x\): \(x = \frac{50}{\tan(41^\circ)}\). We know that \(\tan(41^\circ)\approx0.8693\) (using a calculator). Then, \(x=\frac{50}{0.8693}\approx57.5\) (rounded to one decimal place).

Answer:

The person is approximately \(\boldsymbol{57.5}\) feet from the base of the building.