Question

solve the triangle with the given parts. a = 99.6°, b = 7, c = 11 what is the length of side a? (round to four decimal places.) what is the measure of angle b? ° (round to the nearest tenth.) what is the measure of angle c? ° (round to the nearest tenth.)

Explanation:

Step1: Find side \(a\) using the Law of Cosines

The Law of Cosines formula is \(a^{2}=b^{2}+c^{2}-2bc\cos A\).
Substitute \(b = 7\), \(c = 11\), and \(A=99.6^{\circ}\) into the formula:

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Step2: Find angle \(B\) using the Law of Sines

The Law of Sines formula is \(\frac{\sin B}{b}=\frac{\sin A}{a}\).
We know \(b = 7\), \(a\approx14.0218\), and \(A = 99.6^{\circ}\).

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Step3: Find angle \(C\) using the angle - sum property of a triangle

Since \(A + B+C=180^{\circ}\), then \(C=180^{\circ}-A - B\).
Substitute \(A = 99.6^{\circ}\) and \(B\approx29.5^{\circ}\) into the formula:

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Answer:

The length of side \(a\) is approximately \(14.0218\).
The measure of angle \(B\) is approximately \(29.5^{\circ}\).
The measure of angle \(C\) is approximately \(50.9^{\circ}\).