The distance between two locations, A and B is calculated using a third location C at a distance of 15 miles from location B. If B= 105º and C= 20°, what is the distance, to the nearest tenth of a mile, between locations A and B?

=================================================

Explanation:

See the diagram below. The two given angles B = 105 and C = 20 are used to help find angle A

A+B+C = 180

A+105+20 = 180

A+125 = 180

A = 180-125

A = 55

Then we use the law of sines to find the side length c

sin(A)/a = sin(C)/c

sin(55)/15 = sin(20)/c

c*sin(55) = 15*sin(20) ... cross multiply

c = 15*sin(20)/sin(55)  .... divided both sides by sin(55)

c = 6.26294249724791 .... value is approximate

c = 6.3 ....... rounding to one decimal place

54

step-by-step explanation:

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.