Question

calculating a change in length
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: Find initial distance to building

Use tangent: $\tan(37^\circ) = \frac{130}{d_1}$ → $d_1 = \frac{130}{\tan(37^\circ)}$
Calculate: $\tan(37^\circ) \approx 0.7536$, so $d_1 \approx \frac{130}{0.7536} \approx 172.5$ ft

Step2: Find new distance to building

Use tangent: $\tan(40^\circ) = \frac{130}{d_2}$ → $d_2 = \frac{130}{\tan(40^\circ)}$
Calculate: $\tan(40^\circ) \approx 0.8391$, so $d_2 \approx \frac{130}{0.8391} \approx 154.9$ ft

Step3: Calculate distance difference

Subtract distances: $\Delta d = d_1 - d_2$
$\Delta d \approx 172.5 - 154.9 = 17.6$ ft

Answer:

17.6 ft