Hey,

This question is from a college math placement practice test that I took yesterday and I couldnt for the life of me remember how to evaluate this angle.

"In the right angle shown in the figure below, tan ( θ ) = _____ ?"

it was multiple choice but I only have access to the question itself and the answer which i selected (randomly, may I add =p).

Any help would be much appreciated, answer or otherwise, but i am most interested in the laws/formulas/ideas which allow you to evaluate this.

Thanks a million for any help

EDIT: the placement test is no calculator no notes, btw^^

2. $\displaystyle \tan(\theta)=\dfrac{\text{opp}}{\text{adj}}=\sqrt{ x^2-1}$

3. How did you get a value for the opposite side without adding another variable to the mix though?

The furthest I can get without doing so is:

cos θ = 1 / x

tan θ = sin θ / cos θ = sin θ * x

edit:

The Law of Cosines!!

Lol figured it out, thanks for the little push in that direction

4. The third side of that triangle is $\displaystyle \sqrt{x^2-1}$.

5. Originally Posted by brown399
How did you get a value for the opposite side without adding another variable to the mix though?

The furthest I can get without doing so is:

cos θ = 1 / x

tan θ = sin θ / cos θ = sin θ * x
Pythagoras' theorem is one more way.

Yet another way is

$\displaystyle cos^2\theta+sin^2\theta=1$

$\displaystyle sin^2\theta=1-cos^2\theta$

$\displaystyle sin\theta=\sqrt{1-cos^2\theta}$

$\displaystyle tan\theta=\frac{sin\theta}{cos\theta}$

that can be simplified.
Then you can also use trigonometric identities.