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3 years ago

3. If triangle ABC has the following measurements, find the measure of angle A.

Mathematics

1 answer:

klio [65]3 years ago

5 0

9514 1404 393

Answer:

(a) 42.3°

Step-by-step explanation:

Side 'a' is the shortest of three unequal sides, so angle A will be the smallest angle in the triangle. Its measure can be found from the Law of Cosines.

a² = b² +c² -2bc·cos(A)

cos(A) = (b² +c² -a²)/(2bc) = (21² +25² -17²)/(2·21·25) = 777/1050

A = arccos(777/1050) ≈ 42.3°

The measure of angle A is about 42.3°.

_____

Additional comment

The smallest angle in a triangle can never be greater than 60°. This lets you eliminate choices that exceed that value.

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