Question

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

Answer 1

17.6 feet

Explanation:

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.

Let x be the distance between the building and Diana,

Tan theta = opposite / adjacent side

then tan 37 = 130/x

`tan(37)=(130)/(x) \\xtan(37)= 130\\x=(130)/(tan(37)) =172.5 feet`

Let y be distance between the building and Diana after moving forward,

`tan(40)=(130)/(y) \\ytan(40)= 130\\y=(130)/(tan(40)) =154.9 feet`

now find the distance by subtracting to find how much closer she is to the building

`172.5 - 154.9 = 17.6 ft`