Question

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?

Answer 1

Answer: approximately 6.3 miles

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Step-by-step 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