Q40. Solve triangle ABC using the giv... [FREE SOLUTION]

Chapter 13: Q40. (page 707)

Solve triangle ABC using the given measurements if $\sin A = \frac{1}{3}, C = 90 {}^{鈭�}{and} a = 5$ . Round measure of sides to the nearest tenth and measures of angles to nearest degree.

Short Answer

Expert verified

The solution for triangle ABC is $b = 14.1, c = 15, 鈭� A = 19 {}^{鈭�}{and} 鈭� B = 71 掳$ .

Step by step solution

Step 1. Write down the given parameters of triangle.

The given triangle ABC is shown below whose parameters are represented as $\sin A = \frac{1}{3}, C = 90 {}^{鈭�}{and} a = 5$ .

Step 2. Calculation.

In triangle ABC, $\sin A = \frac{1}{3}, C = 90 {}^{鈭�}{and} a = 5$ .

$\begin{matrix} \sin A = \frac{1}{3} \\ A = \sin^{鈭� 1} (\frac{1}{3}) \\ A = 19 掳 \end{matrix}$

Now, $A = 19 {}^{鈭�}{and} C = 90 掳$ , therefore by angle sum property $鈭� B = 71 掳$ .

By trigonometric ratios in triangle ABC,

$\begin{matrix} \sin A = \frac{1}{3} \\ \frac{a}{c} = \frac{1}{3} \\ \frac{5}{c} = \frac{1}{3} \\ c = 15 \end{matrix}$

Now, in right triangle ABC, plugging for $a = 5, c = 15$ , gives.

$\begin{matrix} c^{2} = a^{2} + b^{2} 鈥塯颈惫别蝉, \\ 15^{2} = 5^{2} + b^{2} \\ b^{2} = 15^{2} 鈭� 5^{2} \\ b = \sqrt{15^{2} 鈭� 5^{2}} \\ b = 14.1 \end{matrix}$

Step 3. Conclusion.

Thesolution for triangle ABC, is $b = 14.1, c = 15, 鈭� A = 19 {}^{鈭�}{and} 鈭� B = 71 掳$ .

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Solve triangle ABC using the given measurements if $\sin A = \frac{1}{3}, C = 90 {}^{鈭�}{and} a = 5$ . Round measure of sides to the nearest tenth and measures of angles to nearest degree.

Short Answer

Step by step solution

Step 1. Write down the given parameters of triangle.

Step 2. Calculation.

Step 3. Conclusion.

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91影视

Solve triangle ABC using the given measurements if sinA=13,C=90and鈭�a=5. Round measure of sides to the nearest tenth and measures of angles to nearest degree.

Short Answer

Step by step solution

Step 1. Write down the given parameters of triangle.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Probability and Statistics

Calculus

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve triangle ABC using the given measurements if $\sin A = \frac{1}{3}, C = 90 {}^{鈭�}{and} a = 5$ . Round measure of sides to the nearest tenth and measures of angles to nearest degree.