SOLUTION: A 5 metre tall sign is placed on top of an office building. From a point on the sidewalk level with the base of the building, the angle of elevation to the top of the sign and the

Algebra ->  Trigonometry-basics -> SOLUTION: A 5 metre tall sign is placed on top of an office building. From a point on the sidewalk level with the base of the building, the angle of elevation to the top of the sign and the       Log On


   

Question 1070065: A 5 metre tall sign is placed on top of an office building. From a point on the sidewalk level with the base of the building, the angle of elevation to the top of the sign and the angle of elevation to the bottom of the sign are 40 degrees and 32 degrees, respectively. Find the height of the building to the nearest metre.
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
This forms two right triangles, sharing the same leg on the bottom.

Draw segment vertically of lengths y+5, and a horizontal segment at right angle to the bottom point, length x. To top of sign is y+5, given angle described 40 degree. height of the building is y, given angle 32 degree.

system%28tan%2832%29=%28y%2B5%29%2Fx%2Ctan%2840%29=y%2Fx%29
Essentially two linear equations in x and y; and you want a solution (value) for y.

You can find an expression for y, and do all the main computations on that:
highlight%28y=5%2Atan%2840%29%2F%28tan%2832%29-tan%2840%29%29%29