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Chapter 13: Q38. (page 707)

Solve triangle ABC using the given measurements if a=4,C=90and鈭�c=9. Round measure of sides to the nearest tenth and measures of angles to nearest degree.

Short Answer

Expert verified

The solution for triangleABC isb=8.1,A=26and鈭�B=64掳.

Step by step solution

01

Step 1. Write down the given parameters of triangle.

The given triangle ABC is shown below whose parameters are represented as a=4,C=90and鈭�c=9.

02

Step 2. Calculation.

In triangle ABC, a=4,C=90and鈭�c=9.

Now, in right triangle ABC,

c2=a2+b2鈥塯颈惫别蝉,92=42+b2b2=92鈭�42b=92鈭�42b=8.1

Now by trigonometric ratios,

cosB=accosB=49B=cos鈭�149B=64掳

Now, C=90and鈭�B=64掳, therefore by angle sum property A=26掳.

03

Step 3. Conclusion.

Thesolution for triangle ABC, is b=8.1,A=26and鈭�B=64掳.

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