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? Ro

Question

2 years ago

14

und your answer to the nearest tenth. 0. 4 radian 1. 0 radian 2. 7 radians 5. 0 radians.

1 answer:

Tcecarenko [31] · Answer 1 · 2023-04-10T22:38:24+03:00

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

<h2>Length of Arc</h2>

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

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

<h2>Explanation</h2>

Given to us

<h3>Assumption</h3>

Let the angle be θ.

<h3>Measure of the Angle</h3>

Substituting the values in the formula of Length of Arc,

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

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

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

<h3>Degree to Radian</h3>

$\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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