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: Find initial distance to building

Use tangent: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$, so $\text{adjacent} = \frac{\text{opposite}}{\tan(\theta)}$.
$\text{Initial distance} = \frac{130}{\tan(37^\circ)}$
$\tan(37^\circ) \approx 0.7536$, so $\frac{130}{0.7536} \approx 172.5$ ft

Step2: Find new distance to building

Use same tangent formula for $40^\circ$.
$\text{New distance} = \frac{130}{\tan(40^\circ)}$
$\tan(40^\circ) \approx 0.8391$, so $\frac{130}{0.8391} \approx 154.9$ ft

Step3: Calculate distance difference

Subtract new distance from initial distance.
$\text{Difference} = 172.5 - 154.9 = 17.6$ ft

Answer:

17.6 ft