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Q30.

Expert-verified

Algebra 2

Found in: Page 707

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

Solve triangle ABC using the given measurements if $B = 27 {}^{\circ}, C = 90 {}^{\circ}{and} b = 7$ . Round measure of sides to the nearest tenth and angles to nearest degree.

The solution for triangle ABC is $a = 13.7, c = 15.4 and ∠ A = 63 °$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Write down the given parameters of triangle.

The given triangle ABC is shown below whose parameters are represented as $B = 27 {}^{\circ}, C = 90 {}^{\circ}{and} b = 7$ .

Step 2. Calculation.

In triangle ABC, $B = 27 {}^{\circ}, C = 90 {}^{\circ}{and} b = 7$ . Therefore, $∠ A = 63 °$ by angle sum property.

Now, trigonometric ratios,

$\begin{matrix} \sin B = \frac{b}{c} \\ \sin 27 ° = \frac{7}{c} \\ c = 7 \csc (27 °) \\ c = 15.4 \end{matrix}$

Now, in right triangle ABC by Pythagoras Theorem.

$\begin{matrix} c^{2} = a^{2} + b^{2} gives, \\ {15.4}^{2} = a^{2} + 7^{2} \\ a^{2} = {15.4}^{2} - 7^{2} \\ a = \sqrt{{15.4}^{2} - 7^{2}} \\ a = 13.7 \end{matrix}$

Step 3. Conclusion.

The solution for triangle ABC, is $a = 13.7, c = 15.4 and ∠ A = 63 °$ .

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