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Chapter 13: Q30. (page 707)

Solve triangle ABC using the given measurements if B=27,鈭�C=90and鈭�b=7. Round measure of sides to the nearest tenth and angles to nearest degree.

Short Answer

Expert verified

The solution for triangle ABC isa=13.7,c=15.4and鈭�A=63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 B=27,鈭�C=90and鈭�b=7.

02

Step 2. Calculation.

In triangle ABC, B=27,鈭�C=90and鈭�b=7. Therefore, 鈭�A=63掳 by angle sum property.

Now, trigonometric ratios,

sinB=bcsin27掳=7cc=7csc27掳c=15.4

Now, in right triangle ABC by Pythagoras Theorem.

c2=a2+b2鈥塯颈惫别蝉,15.42=a2+72a2=15.42鈭�72a=15.42鈭�72a=13.7

03

Step 3. Conclusion.

Thesolution for triangle ABC, is a=13.7,c=15.4and鈭�A=63掳.

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