Question

Consider a triangle ABC like the one below. Suppose that C=83°, a = 43, and b = 44. Solve the triangle.

Answer 1

Answer:

Explanation:

   In a triangle

a / sin A = b / sinB = c / sinC

Putting the values

43 / sin A = 44 / sinB

sinA / sinB = 43 / 44 = 1 / 1.023

A + B = 180 - 83 = 97

sinA / sin ( 97 - A ) = 1 / 1.023

sin 97 cos A - cos 97 sin A = 1.023 sin A

= .9925 cos A + .122 sin A = 1.023 sin A

.9925 cos A = .901 sin A

squaring

.985 cos²A = .8118 sin²A

.985 - .985 sin²A = .8118 sin²A

.985 = 1.7968 sin²A

sinA = .74

A = 47.73

B = 49.27

c / sin C = b / sin B

c = b sinC / sinB

= 44 x sin 83 / sin 49.27

= 44 x .9925 / .7578

= 57.62