Question

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

Explanation:

Step1: Use tangent function for initial distance

Let the initial distance be $x$. $\tan(37^{\circ})=\frac{130}{x}$, so $x = \frac{130}{\tan(37^{\circ})}\approx172.4$ ft.

Step2: Use tangent function for new - distance

Let the new distance be $y$. $\tan(40^{\circ})=\frac{130}{y}$, so $y=\frac{130}{\tan(40^{\circ})}\approx155.0$ ft.

Step3: Calculate the difference

The difference $d=x - y\approx172.4−155.0 = 17.4\approx17.6$ ft.

Answer:

17.6 ft