Question

Solve the triangle. A = 51°, b = 14, c = 6 A. a ≈ 14.9, C ≈ 28.1, B ≈ 100.9 B. a ≈ 11.2, C ≈ 24.1, B ≈ 104.9 C. a ≈ 14.9, C ≈ 24.1, B ≈ 104.9

Answer 1

(B) has the closest values.

Explanation:

Solve the triangle: A = 51°, b = 14, c = 6

A. a ≈ 14.9, C ≈ 28.1, B ≈ 100.9

B. a ≈ 11.2, C ≈ 24.1, B ≈ 104.9

C. a ≈ 14.9, C ≈ 24.1, B ≈ 104.9

Using the cosine rule,

a^2 = b^2+c^2-2bc (cos(A))

= 196+36 - 2(14)(6)cos(51)

= 196+36 - 105.72

= 126.27

a = sqrt(126.27)

= 11.24

using sine rule,

sin(C)/sin(A) = 6/11.24

sin(C) = 6/11.24*sin(51)= 0.41495

C = arcsin(0.41495 = 24.5 degrees, reasonably close to the given value, probably due to the answer used the rounded value of a.

B = 180-51-24.5 =104.5

Out of the given options, only (B) has the correct value of a and C