Solve the problem.
-A surveyor standing 56 meters from the base of a building measures the angle to the top of the building and finds it to be 39°. The surveyor then measures the angle to the top of the radio tower on the building and finds
That it is 49°. How tall is the radio tower?
A) 19.07 m
B) 9.87 m
C) 6.78 m
D) 7.02 m

Question

Quizplus · Accepted Answer

To find the height of the radio tower, we first calculate the total height from the ground to the top of the radio tower using the tangent of the 49° angle, and then subtract the height from the ground to the top of the building (using the 39° angle). Let $ h $ be the height of the building and $ H $ be the total height (building + radio tower). We have:1. $ \tan(39°) = \frac{h}{56} $ and2. $ \tan(49°) = \frac{H}{56} $.Solving these equations gives us:1. $ h = 56 \tan(39°) $2. $ H = 56 \tan(49°) $.The height of the radio tower is $ H - h $.Calculating:1. $ h = 56 \tan(39°) \approx 56 \times 0.80978 \approx 45.35 $ meters2. $ H = 56 \tan(49°) \approx 56 \times 1.15037 \approx 64.42 $ metersTherefore, the height of the radio tower is $ 64.42 - 45.35 \approx 19.07 $ meters.

Solve the Problem. -A Surveyor Standing 56 Meters from the Base of a Base