In △ABC, m∠A=53°, m∠B=17°, and a=27. Find the perimeter of the triangle.

Question

Mathematics

Clarence Soto

1 March, 17:29

In △ABC, m∠A=53°, m∠B=17°, and a=27. Find the perimeter of the triangle.

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Answers (1)

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Weston Nicholson · Answer 1

Using the Law of Sines (sinA/a=sinB/b=sinC/c) and the fact that all triangles have a sum of 180° for their angles.

The third angle is C is 180-53-17=110°

27/sin53=b/sin17=c/sin110

b=27sin17/sin53, c=27sin110/sin53

And the perimeter is a+b+c so

p=27+27sin17/sin53+27sin110/sin53 units

p≈68.65 units (to nearest hundredth of a unit)