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?
I got 1016.66 feet, but that is wrong. What is the correct answer and how would I solve this? Thanks!
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
Thanks! But why wouldn't it be cos120 degrees? Because it's a straight line and 180-60 = 120?
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.
Sorry, I mistyped the question. The 2 roads intersected at 120 degrees. I got 747.48, is this correct? Sorry and thanks again.
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.
To solve this problem, we can use the law of cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.
Let's call the distance from the intersection to your friend's mailbox "x." We are looking for the distance between your mailbox and your friend's mailbox, which is the side opposite the 60-degree angle.
Using the law of cosines, we have:
x^2 = 434^2 + 525^2 - 2 * 434 * 525 * cos(60°)
Simplifying this equation, we get:
x^2 = 188356 + 273375 - 453150 * 0.5
x^2 = 188356 + 273375 - 226575
x^2 = 234156
Taking the square root of both sides, we find:
x ≈ 483.9 feet
Therefore, the distance from your mailbox to your friend's mailbox is approximately 483.9 feet, not 1016.66 feet.
To solve this type of problem, you can use the law of cosines to find the missing side of a triangle when you know the lengths of two sides and the angle between them.