Question

Two sides and an angle (SSA) of a triangle are given. Determine if the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round lengths to the nearest tenth and angle measures to the nearest degree. Length of triangle:B=17, b=13.8, a=15.73

Answer 1

1. c = 28.1, A = 19°, C = 144°

2. c = 2.0, A = 161°, C = 2°

Explanation:

In general, if the given angle is not opposite the longest side, there will be two solutions. That is the case here.

Angle A can be found from the law of sines. It will be ...

A = arcsin(a/b·sin(b)) = arcsin(15.73/13.8·sin(17°)) ≈ arcsin(0.333261) ≈ 19.46°

or the supplement of that, 160.54°.

Angle C will be the angle required to make the sum of angles be 180°, either 143.53° or 2.47°.

Side c will be ...

c = b·sin(C)/sin(B) ≈ 47.2002×sin(C)

either 28.053 or 2.032.

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There are two possible triangles:

(A, C, c) = (19°, 144°, 28.1) or (161°, 2°, 2.0)