Question

Find r. Use law of sine. Round to the nearest tenth.

Answer 1

12

Explanation:

First find the missing angle S

Three angles of a triangle add up to 180°

So m∠S + 81 + 42 = 180

m∠S + 123 = 180

m∠S = 180 - 123 = 57°

Using the law of sines which states that the ratio of each side to the opposite angle is the same for both sides we get

`(r)/(\sin 42) = (q)/(\sin81) = (15)/(\sin 57)\\\\\sin 57 = 0.83867\\\\ (15)/(\sin 57)= (15)/(0.83867)\\\\= 17.88545\\\\`

Hence

`(r)/(\sin 42) = 17.88545\\\\r = 17.88545 * \sin 42\\\\r = 17.88545 * 0.66913\\\\r = 11.9677\\\\r = 12 \textrm{ rounded to the nearest tenth}`