1 Answer

Jelly Bean · Answer 1 · 2023-09-27T22:52:47+0000

Law of Sines

Given a triangle of sides a, b, and c with opposite angles A, B, and C respectively, the law of sines gives the following relationships:

$(b)/(\sin B)=(a)/(\sin A)=(c)/(\sin C)$

We are given a triangle with a = 16, B = 54°, and C = 82°.

To calculate side b, we apply the law of sines with the ratios whose data are available. We have side a, but not angle A.

To find angle A, we use the relationship:

A + B + C = 180°

Recall the sum of the interior angles of a triangle is 180°. Solving for A:

A = 180° - B - C = 180° - 54° - 82°

A = 44°

Now apply the law of sines:

$(b)/(\sin54^o)=(16)/(\sin 44^0)$

Select the last choice.

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