homework help in trigonometric functions

Question

Sighting the top of a building, a surveyor measured the angle of elevation to be 60º. The measurement is taken 200 feet from from the building. Find the building's hight. Express your answer in terms of feet and then round to two decimals places.

Answer 1

The imaginary triangle formed by the given information is a right triangle with the right angle at the base of the building.

 

Thus, we have a triangle with side A = 200 feet, and the angle formed by the hypotenuse and side A = 60^o.

 

We know that the tangent of an angle = opposite ÷ adjacent

 

Thus, tangent of 60^o = opposite ÷ 200 feet; therefore, tangent 60^o · 200 feet = opposite

 

Then, assuming the number is 200.00 feet,

1.732 · 200.00 feet = opposite ≈ 346.41 feet