I need help with a trigonometry question

Question

A tower is located 375 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 27° and that the angle of depression to the bottom of the tower is 20°. How tall is the tower?

Answer 1

construct a triangle with altitude (rotated 90 degrees) of 375 feet and opposite angle = 27+20 = 47 degrees

find the base

angle of elevation =27

angle of depression =20

contruct two right adjoining triangles

top one has angles 27, 90 and 63

bottom one has angles 20, 90 and 70 degrees

height of building =x+y= sum of opposite sides of the two right triangles

= 375tan27 +327tan20 = about 327.56 feet