A ship leaves port and sails at a bearing of 124degrees. Another ship leaves the same port, at the same time, sailing at a bearing of 74degrees. When both ships are 80 miles from the port, how far are they from each other?
use the law of cosines. The included angle is 50°
Pls i need answer: A surveyor observes that the bearing of a beacon O from the beacons P and Q are N30degreeW and N70degreeE respectively. If the bearing of P from Q is 080degree and PQ = 300m calculate (a)the distance PQ (b) the distance O from PQ (c) the bearing of Q from P
To find the distance between the two ships, we can use the Law of Cosines. The Law of Cosines applies to any triangle and relates the lengths of the sides to the cosine of one of the angles.
Let's denote the distance between the two ships as "d". From the given information, we know that the angle between the two ships is (124 - 74) = 50 degrees, and the distances from the port to each ship are 80 miles.
Using the Law of Cosines, we have:
d^2 = (80)^2 + (80)^2 - 2 *(80)*(80)*cos(50)
Now we can solve for d:
d^2 = 6400 + 6400 - 12800 * cos(50)
d^2 = 12800 - 12800 * cos(50)
d^2 = 12800 * (1 - cos(50))
d = sqrt(12800 * (1 - cos(50)))
Using a calculator, we calculate:
d ≈ 94.39 miles
Therefore, the two ships are approximately 94.39 miles apart.