2 roads intersect at an angle of 60 degrees. A friend's mail box is 434 feet from that intersection and your mailbox is on the other road and is 525 feet from the intersection. How far is it from your mailbox to your friend's mailbox?

Question

I got 1016.66 feet, but that is wrong. What is the correct answer and how would I solve this? Thanks!

Answer 1

looks like a direct case of the cosine law

d^2 = 434^2 + 525^2 - 2(434)(525)cos 60°
= 188356 + 275625 - 227850
= 236131
d =√236131 = 485.933

Answer 2

Thanks! But why wouldn't it be cos120 degrees? Because it's a straight line and 180-60 = 120?

Answer 3

The angle formed from its standard position is 60 degree. Unless it says that these angles are in Quadrant 2, then you would have to use 180-60=120.

Answer 4

Sorry, I mistyped the question. The 2 roads intersected at 120 degrees. I got 747.48, is this correct? Sorry and thanks again.

Answer 5

Law of Cosine is useful in Side-Angle-Side such as this question. Since they intersect at 120 degrees, then just plug in cos(120) instead of 60. When I plugged it into the calculator, I got 831.76.