A Question Regarding Trigonometry

Question

For question 7, I have figured out the angles for 2 triangles, the one with RJh and the one with PJh. I don't know what to do after that.

Answer 1

Okay, so look at my outline:

http://sketchtoy.com/60466249

We've got:

$$100^2=x^2+y^2$$ $$h=x\tan 18$$ $$h=y \tan 20$$

Right off the bat, we can substitute the $h$'s:

$$x\tan 18=y \tan 20$$

Welp, let's just solve for one variable. Let's just use $y$ (doesn't matter):

$$y=\frac{x \tan 18}{\tan 20}$$

Plug it in:

$$100^2=x^2+\left(\frac{x \tan 18}{\tan 20}\right)^2$$

Simplify:

$$10000=x^2\left(1+\left(\frac{\tan 18}{\tan 20}\right)^2\right)$$

Very easy to get $x$ now:

$$x \approx 74.5992 \text { m}$$

From $x$, we'll get $h$ to be:

$$h=x \tan 18 \approx 24.2388 \text{ m}$$

If you find $y$ and then find $h$ from there, you'll get the same answer.