If a stick of length 5.18 m is placed so that the ends just touch a circle of radius 10 m, the stick will subtend a 30° angle when viewed from the center of the circle. What does the formula derived in Box 1-1 give you as the length of this stick?
A)1.26 m
B)5.18 m
C)5.24 m
D)11.8 m

Question

Quizplus · Accepted Answer

Using the formula derived in Box 1-1, we know that the length of the stick is equal to 2(r)(sin(θ/2)), where r is the radius of the circle and θ is the angle subtended by the stick at the center of the circle. Plugging in the given values, we have:

length of stick = 2(10)(sin(30/2))
= 2(10)(sin(15))
≈ 5.24 m

Therefore, the best choice is C, 5.24 m.

If a Stick of Length 5