Question

Solve the triangle.

A = 54°, b = 11, c = 8

No triangles possible

a ≈ 13.4, C ≈ 49.6, B ≈ 76.4

a ≈ 13.4, C ≈ 45.6, B ≈ 80.4

a ≈ 9, C ≈ 45.6, B ≈ 80.4

Answer 1

Use cosine law for angle A : \[\large{\cos A = \cfrac{b^2 + c^2 - a^2}{2bc} } \]

Answer 2

\[\large{\cos 54 = \cfrac{11^2 + 8^2 - a^2}{2(11)(8)} }\]

\[\large{0.58 = \cfrac{121 + 64 - a^2 }{176} \\
0.58 = \cfrac{185 - a^2 }{ 176 } \\
(0.58)(176) - 185 = -a^2 \\
102.08 - 185 = -a^2 \\
-82.92 = -a^2 \\
82.92 = a^2 \\
a = \sqrt{82.92} = 9 (approx.) \\ }\]

it is clear from the options that only the third option is having a as 9 units, so it is c)

Answer 3

@tholn,
hope it helped.