Applying Trigonometric Identities and Equations — Test

Question 5 • Precalculus

What are the possible remaining angle measures in triangle ABC with m angle cap A is equal to 40 degrees , AC is equal to 60 , and BC is equal to 45 ?

Answer

m angle cap b almost equal to 59 degrees , m angle cap c almost equal to 81 degrees

m angle cap b almost equal to 121 degrees , m angle cap c almost equal to 19 degrees and m angle cap b almost equal to 59 degrees , m angle cap c almost equal to 81 degrees

No triangle can be formed with these measures.

m angle cap b almost equal to 121 degrees , m angle cap c almost equal to 19 degrees

Explanation

By the sine rule, sin B / 60 = sin 40° / 45, so sin B ≈ 0.857. This gives two possible angles: B ≈ 59° or B ≈ 121°, since angles with the same sine can be supplementary. Using A + B + C = 180°, the corresponding values of C are about 81° and 19°. Therefore, both pairs listed in choice B are possible.

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