Question

An arc of length 8 in. Is intersected by a central angle in a circle with a radius of 3 in. What is the measure of the angle? Round your answer to the nearest tenth. 0. 4 radian 1. 0 radian 2. 7 radians 5. 0 radians.

Answer 1

To solve the problem we must know about the formula of the length of the Arc.

Length of Arc

$\rm{ Length\ of\ Arc = \dfrac{2\pi r \theta}{360^o}$

The angle made by the arc in the center is 2.7 radians.

Explanation

Given to us

• Length of the arc = 8 in.
• radius of the circle = 3 in.

Assumption

Let the angle be θ.

Measure of the Angle

Substituting the values in the formula of Length of Arc,

$\rm{ Length\ of\ Arc = \dfrac{2\pi r \theta}{360^o}$

$8\ in. = \dfrac{2\pi \times 3 \times \theta}{360^o}$

$\theta = \dfrac{360^o\times 8\ in.}{2\pi \times 3 }\\\\ \theta = 152.788^o \approx 152.79^o$

Degree to Radian

$\theta = 152.79^o$

   $=\dfrac{\theta \times \pi}{180^o}$

   $\rm{=2.6666667 \approx 2.7\ radians$

Hence, the angle made by the arc in the center is 2.7 radians.

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