from a point on the edge of the sea one ship is 24km away on a bearing of S50E and another ship is 7km away on a bearing of S60W.how far apart are the ships
You have two sides and the included angle, use law of cosines. I think the angle is 70 deg, check it.
416536
To find the distance between the two ships, we can use the cosine rule.
First, let's visualize the problem. We have a point on the edge of the sea, and from that point, there are two ships located at different distances and directions. Ship A is 24 km away on a bearing of S50E, which means it is located 50 degrees east of south. Ship B is 7 km away on a bearing of S60W, which means it is located 60 degrees west of south.
To calculate the distance between the ships, we need to form a triangle with the two ships and the point on the edge of the sea. The angle between the direction of Ship A and Ship B can be found by adding the bearings of the two ships: S50E + S60W = 110 degrees.
Now, let's use the cosine rule:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case, 'c' represents the distance between the two ships, and 'a' and 'b' represent the distances of Ship A and Ship B from the point on the edge of the sea, respectively. 'C' is the angle between the two directions of the ships.
Here's how we can calculate the distance between the ships:
c^2 = 24^2 + 7^2 - 2 * 24 * 7 * cos(110 degrees)
c^2 = 576 + 49 - 336 * cos(110 degrees)
Now, we can evaluate the expression:
c^2 ≈ 625 - 336 * (-0.342)
c^2 ≈ 625 + 115.152
c^2 ≈ 740.152
Taking the square root of both sides, we get:
c ≈ √(740.152)
c ≈ 27.18
Therefore, the distance between the two ships is approximately 27.18 km.