Question

A boat is 400 feet away from one dock and 500 feet away from another dock the angle between the two paths is 45. What is the approximate distance between the docks ?

Answer 1

Use the law of cosines. Let
`x` be the distance between the docks, which forms a third leg of a triangle for which the angle opposite it has measure 45 degrees. The other two legs have lengths 400 ft and 500 ft. So

`x^2=400^2+500^2-2\cdot400\cdot500\cos45^\circ`

`\implies x\approx356.59\,\mathrm{ft}`