Diana works in a building that is 130 feet tall. She is outside, looking up at the building at an angle of 37° from her feet to the top of the building.

If Diana walks forward and her angle looking to the top of the building changes to 40°, how much closer is she to the building? Round the answer to the nearest tenth of a foot.

10.3 ft
17.6 ft
30.2 ft
97.2 ft

9514 1404 393

  17.6 ft

Step-by-step explanation:

The relation between angles and distances in the relevant triangle is ...

  Tan = Opposite/Adjacent

Then the distance to the building from the observation point is ...

  Adjacent = Opposite/Tan

We want to find the difference between the two observation point distances. That will be ...

  difference = (130 ft)/tan(37°) -(130 ft)/tan(40°)

  = (130 ft)(1/tan37° -1/tan(40°) ≈ (130 ft)(1.32704 -1.19175)

  ≈ (130 ft)(0.13529) ≈ 17.6 ft

Diana is about 17.6 ft closer at her second observation point.