From a ship, the angle of elevation of a point, A, at the top of a cliff is 21°. After the ship has sailed 2,500 feet directly toward the foot of the cliff, the angle of elevation of ∠A is 47°. (Assume the cliff is perpendicular to the ground.)
Point B is where the 21 degree angle of elevation was taken. Point C is where the 47 degree angle of elevation was taken. Point D is at the base of the cliff. You now have a large triangle ABD Two smaller triangles ABC and ACD Putting in angles: Angle BCA = 133 degrees, Angle BAC = 26 degrees Considering triangle ABC: a/Sin A = b/Sin B 2500/sin(26) = b/Sin(21) Cross multiply.
(2500 * sin(21))/sin(26) = b b (Side AC) = 2043.75m Considering triangle ACD This is right angled at D sin = Opposite/Hypotenuse. sin(47) = Opposite/2043.75 Opposite = sin(47) * 2043.75 Opposite = 1494.7m This is the height of the cliff.
