SOLUTION: An employee looks out his office window at a factory across the street. He estimates his office building and the factory building are 60 ft apart, the angle of depression to the ba

Algebra ->  Formulas -> SOLUTION: An employee looks out his office window at a factory across the street. He estimates his office building and the factory building are 60 ft apart, the angle of depression to the ba      Log On


   



Question 1084346: An employee looks out his office window at a factory across the street. He estimates his office building and the factory building are 60 ft apart, the angle of depression to the base of the factory is 62°, and the angle of elevation to the top of the factory building is 23°.
How tall is the factory across the street?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You have 2 right triangles with a common side.
The common side is the shortest distance from the employee to
the other building.
Using the given data, I can say:
(1) +tan%28+62+%29+=+a%2F60+
(2) +tan%28+23+%29+=+b%2F60+
(3) +a+%2B+b+ = the height of the factory building
-----------------------
(1) +1.8807+=+a%2F60+
(1) +a+=+112.844+
and
(2) +.4245+=+b%2F60+
(2) +b+=+25.468+
and
(3) +a+%2B+b+=+112.844+%2B+25.468+
(3) +a+%2B+b+=+138.312+
Convert the decimal to inches
+.312%2A12+=+3.7+
The factory is 138 ft 4 in tall approximately
You can get another opinion, also