from a point of 100ft from the base of the cliff, Kim measures the angle of elevation to a ledge on the side of the cliff to be 42 degrees. Find the height of the ledge from the base of the cliff, to the nearest foot

You have been given a right triangle. The side adjacent to the 42 degree angle is 100'; call the side opposite the 42 degree angle h, the height of the cliff.

tan 42 = h/100 => h = 100(tan 42) = 100(0.900) So h = 90 feet.