In the figure, we can see that the indicated distance of the sailboat from the lighthouse is the side of the triangle opposite the right angle. Therefore, we are looking for the length of the hypotenuse of the triangle.
To get the hypotenuse, we will use the Pythagorean Theorem.
where c = hypotenuse and "a" and "b" are the legs of the triangle.
Given in the figure are the legs of the triangle which are 50 km and 130 km. Let's plug these into the equation above.
Then, solve.
Square each leg of the triangle.
Add the numbers under the radical sign.
Get the square root of 19, 400.
Therefore, the distance of the sailboat from the lighthouse is approximately 139.3 km.