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In ΔABC, a = 9.3 inches, mm∠B=75° and mm∠C=17°. Find the length of b, to the nearest 10th of an inch.

User Kaydeen
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The length of side b is approximately 8.8 inches.

The law of sines asserts that in any triangle ABC: In order to find the length of side b in any triangle ABC:

A/Sin = B/Sin + C/Sin

where the side lengths are a, b, and c and the angles are a, b, and c.

We are informed of the following:

9.3 inches, so a

B = 75°\sC = 17°

We can apply the ratio to determine the length of b:

b/sin B equals a/sin A

After solving for b and substituting in the provided values, we obtain:

75° b/sin = 9.3° sin A

b = (9.3*sin75°) / sinA

We can use the fact that a triangle's angles sum to 180° to determine sin A:

A + B + C = 180°

A + 75° + 17° = 180°

A = 88°

If we replace with sin 88° and sin 75°, we obtain:

B is equal to (9.3 * sin 75°)/sin 88°.

b=8.8 inches (rounded to the nearest 10th of an inch)

As a result, side B measures around 8.8 inches long.

User Kevin Yang
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