How tall is this billboard (Geometry)?

Question

A billboard is on top of a building. I am 140.5 feet from the building. I measure the angle of elevation of the bottom of the billboard as 40 degrees and the angle of elevation of the top of the billboard as 47.6 degrees.

How tall is the billboard?

Answer 1

this is simple trigonometry if you say let the height equal x than you can say well for 40degress you have the opposite and the adjacent therefore we have to use tan. so the equation would be tan40=x/140.5 then you need to get the x all by its self so you make the eqution x=tan40 times 140.5 then you figuire it out on your calculator and the answer is...117.8934982 feet high    if rounded off the billboard is 118 feet high