Q10. Solve triangle ABC using the giv... [FREE SOLUTION]

Chapter 13: Q10. (page 706)

Solve triangle ABC using the given measurements if $B = 56 {}^{鈭�}, C = 90 {}^{鈭�}{and} c = 16$ . Round measure of sides to the nearest tenth and angles to nearest degree.

Short Answer

Expert verified

The solution for triangle ABC is $a = 8.9, b = 13.3 and A = 34 掳$ .

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 $B = 56 {}^{鈭�}, C = 90 {}^{鈭�}{and} c = 16$ .

Step 2. Calculation.

In triangle ABC, $B = 56 {}^{鈭�}, C = 90 {}^{鈭�}{and} c = 16$ . Therefore, $鈭� A = 34 掳$ by angle sum property.

Now, trigonometric ratios,

$\begin{matrix} \sin B = \frac{b}{c} \\ \sin 56 掳 = \frac{b}{16} \\ b = 16 \sin (56 掳) \\ b = 13.3 \end{matrix}$

Now, in right triangle ABC,

$\begin{matrix} c^{2} = a^{2} + b^{2} 鈥塯颈惫别蝉, \\ 16^{2} = a^{2} + {13.3}^{2} \\ a^{2} = 16^{2} 鈭� {13.3}^{2} \\ a = \sqrt{16^{2} 鈭� {13.3}^{2}} \\ a = 8.9 \end{matrix}$

Step 3. Conclusion.

Thesolution for triangle ABC, is $a = 8.9, b = 13.3 and A = 34 掳$ .

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91影视

Solve triangle ABC using the given measurements if $B = 56 {}^{鈭�}, C = 90 {}^{鈭�}{and} c = 16$ . Round measure of sides to the nearest tenth and 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 B=56,鈭�C=90and鈭�c=16. Round measure of sides to the nearest tenth and 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

Calculus

Pure Maths

Theoretical and Mathematical Physics

Logic and Functions

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Solve triangle ABC using the given measurements if $B = 56 {}^{鈭�}, C = 90 {}^{鈭�}{and} c = 16$ . Round measure of sides to the nearest tenth and angles to nearest degree.