To measure a stone face carved on the side of a mountain two

To measure a stone face carved on the side of a mountain, two sightings 467 feet from the base of the mountain are taken. If the angle of elevation to the bottom of the face is 23 degrees and the angle of elevation to the top of the face is 54 degree, what is the height of the stone face in feet?

Solution

given the angle of elevation to the top of the face is 54 degree

  the angle of elevation to the bottom of the face is 23 degrees

  467 feet from the base of the mountain are taken

t = 467tan54 = distance to top of face
b = 467tan23 = distance to bottom of face
t-b = height of face = 467(tan54 - tan23) = 444.54062 feet