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?

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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

the answer is 0.000652422

but if you ment to ask what is 6131 divided by 4, it is 1532.75.

step-by-step explanation:

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west