Due to the curvature of the earth, the maximum distance D that you can see from the top of a tall building of height h is estimated by the formula $D = \sqrt { 2 r h + h ^ { 2 } }$ where r = 3960 mi is the radius of the earth and D and h are also measured in miles. How far can you see from the observation deck of a tower, 955 ft above the ground? Round the answer to one decimal place
A) 37.8 mi
B) 73.8 mi
C)1428.8 mi
D)428.8 mi
E)none of these

Question

Quizplus · Accepted Answer

First, convert the height from feet to miles: 955 ft = 955/5280 mi. Then, use the formula $D = \sqrt{2 \times 3960 \times (955/5280) + (955/5280)^2}$ to calculate D. The result is approximately 37.8 mi.

Due to the Curvature of the Earth, the Maximum Distance D=2rh+h2D = \sqrt { 2 r h + h ^ { 2 } }D=2rh+h2​

Due to the Curvature of the Earth, the Maximum Distance $D = \sqrt { 2 r h + h ^ { 2 } }$