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elixir [45]
2 years ago
14

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

Mathematics
1 answer:
klio [65]2 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°.

_____

<u><em>Additional comment</em></u>

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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