SOLUTION: From the top of an office building 72 ft high, the angle of elevation to the top of an apartment building across the street is 31°. From the base of the office building, the angle

Algebra ->  Trigonometry-basics -> SOLUTION: From the top of an office building 72 ft high, the angle of elevation to the top of an apartment building across the street is 31°. From the base of the office building, the angle      Log On


   

Question 1205240: From the top of an office building 72 ft high, the angle of elevation to the top of an apartment building across the street is 31°. From the base of the office building, the angle of elevation is 46°
• How tall is the apartment building?
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Draw the two right triangles according to the description.
Label everything as described.


Should be lower right triangle vertical leg 72 feet, the two nonright angles 46 and 44 degrees.
Upper right-triangle the nonright angles 31 degrees and 59 degrees.
The two triangles share a horizontal leg.

If x is the length of the shared horizontal leg, then
system%28sin%2846%29%2F72=sin%2844%29%2Fx%2Cand%2Csin%2859%29%2Fx=sin%2831%29%2Fy%29

You don't need the x value. Substitute in order to find and evaluate y.
Question asks for y+72.