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. BAC is 112 degree and the measure of Z ACB is 44 degree. What is the width of the crater? (Simplify your answer. Type an integer or decimal rounded to the nearest hundredth as needed.)

Solution

the width of crater is the length of AB

since A and B are on opposite sides

so we know two angles

A= 112 degree and C=44

so sum of angles in a triangle is 180 degree

A+B+C=180

112 +B+44=180

156+B=180

B=180 -156

B= 24 degree

now By sine law

a/sinA = b/sinB = c/sinC

here a= length of BC

b=length of AC

c=length of AB

we know b=44 meter

so b/sinB = c/sinC

44/sin24 = c/sin44

30.565/sin24 = c

c = 75.15 meter

the width of crater = 75.15 meters = 75 meter (approximating)