Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
-A wheel with a 32 -inch radius is marked at two points on the rim. The distance between the marks along the wheel is found to be 16 inches. What is the angle (to the nearest tenth of a degree) between the radii to the two marks?
A) $28.6 ^ { \circ }$
B) $26.6 ^ { \circ }$
C) $24.6 ^ { \circ }$
D) $30.6 ^ { \circ }$

Question

Quizplus · Accepted Answer

The circumference of the earth is $2\pi r = 2\pi (6400) = 40212$ km. The distance between the marks on the wheel is 16 inches, or $\frac{16}{12} = \frac{4}{3}$ feet. The circumference of the wheel is $2\pi r = 2\pi (32/12) = \frac{32\pi}{6} = \frac{16\pi}{3}$ feet. The angle between the radii to the two marks is $\frac{4/3}{16\pi/3} = \frac{1}{4\pi} \approx 0.0796$ radians, or $0.0796 \cdot 180/\pi \approx 4.56^\circ$.

Assume That the Cities Lie on the Same North-South Line 28.6∘28.6 ^ { \circ }28.6∘

Assume That the Cities Lie on the Same North-South Line $28.6 ^ { \circ }$