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

Answer:

17.6 feet

Step-by-step 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

 $tan(37)=\frac{130}{x} \\xtan(37)= 130\\x=\frac{130}{tan(37)} =172.5 feet$

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

$tan(40)=\frac{130}{y} \\ytan(40)= 130\\y=\frac{130}{tan(40)} =154.9 feet$

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

$172.5 - 154.9 = 17.6 ft$