# Math Help - Trig question help

1. ## Trig question help

For this question, how would I find h or the height using trig. I'm assuming you need x but how would I find that?

Can some please explain it to me simply? I would appreciate it a lot. I'm just getting use to trig so I don't know any complicated things yet..... Thanks!!

2. Originally Posted by Dgb186
For this question, how would I find h or the height using trig. I'm assuming you need x but how would I find that?

Can some please explain it to me simply? I would appreciate it a lot. I'm just getting use to trig so I don't know any complicated things yet..... Thanks!!
$\tan(35) = \frac{h}{x}$

$\tan(20) = \frac{h}{x+500}$

two equations, two unknowns ... solve the system algebraically.

3. Originally Posted by Dgb186
For this question, how would I find h or the height using trig. I'm assuming you need x but how would I find that?

Can some please explain it to me simply? I would appreciate it a lot. I'm just getting use to trig so I don't know any complicated things yet..... Thanks!!
Using skeeter's equations:
$\tan(35) = \frac{h}{x}$
$\tan(20) = \frac{h}{x+500}$

isolate x
$x = \dfrac{h}{tan(35)}$

sub in 2nd equation
$\tan(20) = \dfrac{h}{ \dfrac{h}{tan(35)} +500}$

1 equation 1 unknown

4. Thank-you for your replies!! To solve the system algebraically do you mean something like this?

tan(20)* (500+x) = tan 35(x) ?

5. Originally Posted by Dgb186
Thank-you for your replies!! To solve the system algebraically do you mean something like this?

tan(20)* (500+x) = tan 35(x) ?
That will produce a value for x.
What you are seeking is the variable h.
After you find x, then use it to determine h.

$\tan(20) \cdot (500+x) =x \tan(35)$

$500 \tan(20) + x \tan(20) =x \tan(35)$

$500 \tan(20) = x \tan(35) - x \tan(20)$

$500 \tan(20) = x \left(\tan(35) - \tan(20)\right)$

$\dfrac{500 \tan(20)}{\left(\tan(35) - \tan(20)\right)} = x$