Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
-A pendulum swinging through a central angle of $76 ^ { \circ }$ completes an arc of length $14.3 \mathrm {~cm}$. What is the length of the pendulum? Round to the nearest hundredth.
A) $10.68 \mathrm {~cm}$
B) $10.88 \mathrm {~cm}$
C) $10.78 \mathrm {~cm}$
D) $10.58 \mathrm {~cm}$

Question

Quizplus · Accepted Answer

The length of the pendulum can be found using the formula for arc length: $ s = r \theta $, where $ s $ is the arc length, $ r $ is the radius (length of the pendulum), and $ \theta $ is the central angle in radians. Convert $76^\circ$ to radians: $76^\circ \times \frac{\pi}{180} = \frac{19\pi}{45}$. Then, solve for $ r $: $ r = \frac{s}{\theta} = \frac{14.3}{\frac{19\pi}{45}} \approx 10.78 \mathrm{~cm} $.

Assume That the Cities Lie on the Same North-South Line 76∘76 ^ { \circ }76∘

Assume That the Cities Lie on the Same North-South Line $76 ^ { \circ }$