Question

Find AC and BC. Answers: 14.94 13.46 11.10 10 Please help.

Answer 1

Step-by-step explanation:

Use Sine rule.

$\frac{ac}{ \sin(b) } = \frac{ab}{ \sin(c) } \\ \frac{ac}{ \sin(90) } = \frac{10}{ \sin(42) } \\ ac \sin(42) = 10 \sin(90) \\ ac = \frac{10 \sin(90) }{ \sin(42) } \\ ac = 14.9 \: units \: (3s.f)$

Angle A + angle B + angle C = 180 (sum of angles in triangle)

Angle A + 90 + 42 = 180

Angle A + 132 = 180

Angle A = 180 - 132

= 48

$\frac{bc}{ \sin(a) } = \frac{ab}{ \sin(c) } \\ \frac{bc}{ \sin(48) } = \frac{10}{ \sin(42) } \\ bc \sin(42) = 10 \sin(48) \\ bc = \frac{10 \sin(48) }{ \sin(42) } \\ = 11.1units (3sf)$