Question

Ship A is 14 km from a lighthouse. Ship B is 30 km from the same lighthouse. The angle between ship A and ship B at the lighthouse is 109 degrees. How far is ship A from ship B?

Answer 1

The distance between Ship A and Ship B is approximately 37.75 km.

Step-by-step explanation:

You can use the Law of Cosines to find the distance between Ship A and Ship B. The Law of Cosines states:

c^2 =a^2 +b^2 −2abcos(C)

Where:

c is the side opposite the angle C, a and b are the other two sides.

In this case:

a is the distance from Ship A to the lighthouse (14 km),

b is the distance from Ship B to the lighthouse (30 km),

C is the angle between Ship A and Ship B at the lighthouse (109 degrees).

Let d be the distance between Ship A and Ship B. So,

d is the side opposite the given angle.

d^2 =14^2 +30^2 −2×14×30×cos(109∘ )

Now, you can calculate d:

d^2 =196+900−2×14×30×cos(109∘)

d^2 =1096−2×14×30×cos(109∘ )

d^2 ≈1424.8

d≈ 1424.8​

d≈37.75km

Therefore, Ship A is approximately 37.75 km from Ship B.