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.

The height of the cliff is 1,495 feet.

Step-by-step explanation:

50 is the least number for x it makes the equation equal 45