Question

1. civil engineering the angle of elevation from an observer to the bottom edge of the delaware river drawbridge observation deck located 200 ft from the observer is 30°. the angle of elevation from the observer to the top of the observation deck is 40°. what is the height of the observation deck?

Explanation:

Step1: Find height to bottom edge

Let \( h_1 \) be height to bottom edge. Using \( \tan(30^\circ)=\frac{h_1}{200} \), so \( h_1 = 200\tan(30^\circ) \). \( \tan(30^\circ)=\frac{\sqrt{3}}{3}\approx0.577 \), so \( h_1\approx200\times0.577 = 115.4 \) ft.

Step2: Find height to top edge

Let \( h_2 \) be height to top edge. Using \( \tan(40^\circ)=\frac{h_2}{200} \), \( \tan(40^\circ)\approx0.839 \), so \( h_2\approx200\times0.839 = 167.8 \) ft.

Step3: Calculate deck height

Deck height \( h = h_2 - h_1 \approx167.8 - 115.4 = 52.4 \) ft. (Or use exact formula: \( h = 200(\tan40^\circ - \tan30^\circ) \))

Answer:

The height of the observation deck is approximately \( \boldsymbol{52.4} \) feet (or using exact calculation: \( 200(\tan40^\circ - \tan30^\circ)\approx52.4 \) ft).