Given
two angles (150° and 12°) and the shortest side (12 cm) of a triangle
Find
the second-shortest side
Solution
Strategy: Make use of the Law of Sines to find missing side lengths when angles are known. To find the third angle, make use of the sum of angles of a triangle.
The sum of angles of a triangle is 180°, so we have
... 150° + 12° + C = 180°
... C = 180° - 162° = 18°
The law of sines tells us
... c/sin(C) = b/sin(B)
... c = sin(C)·b/sin(B) = sin(18°)·(10 cm)/sin(12°)
... c ≈ 14.9 cm
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We are calling the sides a, b, c. We are calling the angles opposite those sides A, B, and C.