Points A and B are on opposite sides of a lunar crater Point

Points A and B are on opposite sides of a lunar crater. Point C is 44 meters from point A. The measure of angle BAC is 111 degrees° and the measure of angle ACB is 40 degrees°. What is the width AB of the crater in meters?

Solution

angle BAC is 111 degrees° and the measure of angle ACB is 40 degrees°

therefore angle ABC = 180 - ( 111+40) = 29 degrees

now applying law of sines to find the missing side

AB / sin 40 = AC / sin 29

AB = sin 40 * ( 44 / sin 29 ) = 58.33 metres

therefore , width AB of crater = 58.33 metres approx