Question

An offshore lighthouse is 2 kilometers from a Coast Guard station C and 2.5 kilometers from a hospital H near the shoreline. If the angle formed by light beams to C and H is 143o, what is the distance CH (by sea) between the Coast Guard station and the hospital?

Answer 1

4.3 km

Explanation:

The law of cosines can be used to find the desired distance. If we call the lighthouse position point L, then we have ...

CH² = LC² +LH² -2·LC·LH·cos(L)

CH² = 2² +2.5² -2·2·2.5·cos(143°) = 10.25 -10cos(143°) ≈ 18.2364

CH ≈ √18.2364 ≈ 4.27 . . . . km

The distance CH is about 4.3 km.