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Question

Solve ΔABC. Round decimal answers to the nearest tenth. m∠B = 25°, a = 8, c = 3.

Solution

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2.8 (8 ratings)
Answered 2 years ago
2.8 (8 ratings)
Answered 2 years ago
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Use the Law of Cosines to find bb:

b2=a2+c22accosBb2=82+32283cos25b2=7343.5b=29.5b5.4\begin{align*} b^2&=a^2+c^2-2ac\cos B \tag{Law of Cosines}\\ b^2&=8^2+3^2-2\cdot 8\cdot3 \cdot \cos 25^{\circ} \tag{Substitute}\\ b^2&=73-43.5\\ b&=\sqrt{29.5} \tag{Find the positive square root}\\ b&\approx 5.4 \tag{Use a calculator}\\ \end{align*}

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