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radian measure of the angle formed by its edges, Trigonometry

by Jose
(Carson)











































A slice of pizza leftover from last night has a radius of 7 inches, and the outer crust edge is 4 inches long. What is the radian measure of the angle formed by its edges? Give an exact answer.

Comments for radian measure of the angle formed by its edges, Trigonometry

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Apr 01, 2010
Angle in Radians
by: Staff

The problem


A slice of pizza leftover from last night has a radius of 7 inches, and the outer crust edge is 4 inches long. What is the radian measure of the angle formed by its edges? Give an exact answer.


The solution

Hi Jose,


The fastest way (not the only way) to compute the angle in radians is to use the following formula:

(Radius) x (Angle in Radians) = (Length of Arc)



To solve for the "Angle in Radians", simply divide both sides of the equation by “Radius”

(Radius) x (Angle in Radians) /(Radius) = (Length of Arc) /(Radius)

(Angle in Radians) = (Length of Arc)/(Radius)



Use the formula for “Angle in Radians” (above) to compute the answer to your problem

Length of Arc = 4 inches
Radius = 7 inches

(Angle in radians) = (Length of Arc)/(Radius)

Angle in radians = (4 inches)/( 7 inches)

Angle in radians = (4)/( 7)

Angle in radians = 0.571428571429



The final answer is:

Angle formed by the edges of the slice of pizza = 0.571428571429 radians



One way to think about the problem is this:

If the arc of the outer crust of the slice of pizza did equal the radius, the angle formed by the edges of the pizza would be exactly 1 radian.

In your problem the arc and the radius are not equal. The arc only equals 4 inches, while the radius equals 7 inches.

Therefore, the angle formed by the edges of the pizza would be 4/7 of 1 radian, or .57 radians.


Staff
www.solving-math-problems.com

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