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vredina [299]
3 years ago
7

Given the triangle below, what is m < b, rounded to the nearest tenth?

Mathematics
1 answer:
ahrayia [7]3 years ago
3 0

Option A:

m∠B = 42.1°

Solution:

Given data:

b = 18, c = 15 and m∠C = 34°

Using sine formula:

$\frac{b}{\sin B}=\frac{c}{\sin C}

Substitute the given values.

$\frac{18}{\sin B}=\frac{15}{\sin 34^\circ}

Do cross multiplication.

${18}  \times {\sin 34^\circ}={15}  \times{\sin B}

Divide by 15 on both sides.

$\frac{{18}  \times {\sin 34^\circ}}{15} =\frac{{15}  \times{\sin B}}{15}

$\frac{{6}  \times0.559}{5} =\sin B

$0.6708=\sin B

$\sin ^{-1}0.6708= B

42.1^\circ =B

Switch the sides.

m∠B = 42.1°

Option A is the correct answer.

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