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Q22.

Expert-verified

Geometry

Found in: Page 432

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

Use a calculator or the trigonometry table on page311 to find the area of each figure to the nearest tenth.

The area of given figure is approximately $34.3$ square unit.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

Hypotenuse=10 and $θ = 54^{\circ}$

Step 2. Concept Used.

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Use trigonometric Ratios

$\begin{array}{l} \cos θ = \frac{A d j a c e n t}{H y p o t e n u s e} \\ \cos 54^{\circ} = \frac{BC}{A C} \\ \cos 54^{\circ} = \frac{BC}{12} \\ B C = 7.0536 \end{array}$

Base $= 7.0536$

Step 3. Find the Height of triangle.

$\begin{array}{l} \tan 54^{\circ} = \frac{AB}{B C} \\ \tan 54^{\circ} = \frac{AB}{7.0536} \\ A B = 7.0536 \times 1.3764 \\ A B = 9.708 \end{array}$

Height $= 9.708$

Step 4. Find the area of triangle.

Area of triangle can be found using the formula

$\begin{matrix} A = \frac{1}{2} b h \\ = \frac{1}{2} (7.053) (9.708) \\ = 34.335 \\ \approx 34.3 \end{matrix}$

Therefore, the area of given figure is $34.2$ Square unit.

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