Nicole shines a light from a window of a lighthouse on a cliff 250 feet above the water level. Nick 10 feet above the water leve
l in a ship off shore, finds that the angle of elevation of the light is 3°. Find the length of the line of sight (light beam) from the ship to Nicole.
If we draw the triangle, the opposite side to 3° angle would be "10" less than total height of 250 because Nick is 10 feet above water level, so that side will be:
250 - 10 = 240
The hypotenuse of the triangle is the length of line of sight. We can call this "x".
So, using trigonometric ratio of sine (opposite/hypotenuse), we can write:
Now, we cross multiply and solve for x, line of sight length: