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

Question

3 years ago

11

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.

Mathematics

1 answer:

Olegator [25] · Answer 1 · 2022-09-18T16:54:42+03:00

Answer:

Let x be her initial distance from the building, then tan 37 = 130/x

x = 130/tan 37 = 130/0.7536 = 172.5 feet

Let y be her distance from the building after moving forward, then

tan 40 = 130/y

y = 130/tan 40 = 130/0.8391 = 154.9

After moving forward, she is 172.5 - 154.9 = 17.6 ft closer.