Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Area of a Segment Find the area of the segment (shaded in blue in the figure) of a circle whose radius is 8 feet, formed by a central angle of $70 °$ .
[Hint: Subtract the area of the triangle from the area of the sector to obtain the area of the segment.]

The area of the segment is 9.03 square feet.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The given figure is:

Step 2. Determine the area of the sector.

Area of the sector is:

$\begin{array}{rcl} A_{1} & = & \frac{θ}{360 °} \times π r^{2} \\ = & \frac{70 °}{360 °} \times π \times (8)^{2} \\ = & 39.0953 . . . \\ \approx & 39.10 \end{array}$

Step 3. Determine the area of the triangle.

The area of a triangle is:

$\begin{array}{rcl} A_{2} & = & \frac{1}{2} a b \sin C \\ = & \frac{1}{2} (8) (8) \sin (70 °) \\ = & 30.0701 . . . \\ \approx & 30.07 \end{array}$

Step 4. Determine the area of the segment.

Subtract the area of the triangle from the area of the sector to obtain the area of the segment.

$\begin{array}{rcl} A & = & A_{1} - A_{2} \\ = & 39.10 - 30.07 \\ = & 9.03 \end{array}$

The area of the segment is 9.03 square feet.

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Area of a Segment Find the area of the segment (shaded in blue in the figure) of a circle whose radius is 8 feet, formed by a central angle of $70 °$ .
[Hint: Subtract the area of the triangle from the area of the sector to obtain the area of the segment.]

Step by Step Solution

Step 1. Given information.

Step 2. Determine the area of the sector.

Step 3. Determine the area of the triangle.

Step 4. Determine the area of the segment.

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Area of a Segment Find the area of the segment (shaded in blue in the figure) of a circle whose radius is 8 feet, formed by a central angle of 70°.[Hint: Subtract the area of the triangle from the area of the sector to obtain the area of the segment.]

Step by Step Solution

Step 1. Given information.

Step 2. Determine the area of the sector.

Step 3. Determine the area of the triangle.

Step 4. Determine the area of the segment.

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Area of a Segment Find the area of the segment (shaded in blue in the figure) of a circle whose radius is 8 feet, formed by a central angle of $70 °$ .
[Hint: Subtract the area of the triangle from the area of the sector to obtain the area of the segment.]