# Math Help - Applications of Right Triangles

1. ## 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....

2. 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 $\angle ACB = 45^o,\;AB = BC = x$

In right triangle $ABD\!:\;\;\tan30^o \:=\:\frac{x}{x+20}$

Solve for $x\!:\;\;x \;=\;\frac{20\tan30^o}{1 - \tan30^o}$

Since $\tan30^o \,=\,\frac{1}{\sqrt{3}}$, we have: . $x \;=\;\frac{20\cdot\frac{1}{\sqrt{3}}}{1 - \frac{1}{\sqrt{3}}} \;=\;10(\sqrt{3}+1) \;\approx\;27.3$ ft.

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