Thread: Applications of Right Triangles

24.) The angle of elevation of a flagpole from a point level with its base is 45 degrees. from a point 20 ft. further away, the angle of elevation is 30 degrees. What is the hight of the flagpole to the nearest 0.1 ft.?


I did:

x*tan(45) = (x + 20)*tan(30)
x*tan(45) = x*tan(30) + 20tan(30)
x*tan(45) - x*tan(30) = + 20tan(30)
x(tan45 - tan30) = 20tan(45)
x = 20tan(30)/tan(45)-tan
x = 27.29

or is it:

x*tan(30) = (x - 20)*tan(45)
x*tan(30) = x*tan(45) -20tan(45)
x*tan(30) - tan(45) = -20tan(45)
x(tan30 - tan45) = -20tan(45)
x = -20tan(45)/tan(30) - tan(45)
x = 47.28

I don't know which one is right....

Hello, lax600!

The problem is easier than you think ... Note that 45° angle!

The angle of elevation of a flagpole from a point level with its base is 45°.
From a point 20 ft. further away, the angle of elevation is 30°.
What is the height of the flagpole to the nearest 0.1 ft.?

Code:

    A *
      | * *
      |   *   *
      |     *     *
    x |       *       *
      |         *         *
      |           *           *
      |         45° *         30° *
      * - - - - - - - * - - - - - - - *
      B       x       C      20       D

Since

In right triangle

Solve for

Since , we have: . ft.

so my first answer works... but why not my 2nd answer?