Question

WORTH MANY POINTS The length of one of the sides of a triangle is equal to 1m, the measurement of adjacent angles are 30º and 45º. Give exact measurements for the lengths of the other sides of the triangle. (Round answer to the nearest .001)

Answer 1

• 0.518 m, 0.732 m

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Given

One side and two adjacent angles of a triangle:

• a = 1 m,
• B = 30°, C = 45°.

Find the missing sides of the triangle

First, find the opposite angle to side a:

• A = 180° - (30° + 45°) = 180° - 75° = 105°

Use the law of sines and work out the side lengths:

• a/sin A = b/sin B = c/sin C ⇒
• 1 / sin 105° = b/sin 30° = c / sin 45°

Side b is:

• b = sin 30 / sin 105 = 0.518 m (rounded)

Side c is:

• c = sin 45 / sin 105 = 0.732 m (rounded)