Problem
Express the length a, b, c, and d in the figure in terms of the trigonometric ratios of $θ$. (See the image below)
Progress
I can figure out $c$ usng the pythagorean theorem. $a^2+b^2=c^2$ which would be $2$. Is that correct? How do I solve the rest?
Best Answer
I have marked 5 points P,Q,R,S,T in your diagram.
Consider the triangle formed by points P, S and T. Do you agree that
It is a right-angle triangle, so apply Pythagoras theorem,
We get $b^2+1^2=c^2$
We know that $\sin \theta=\Large \frac{\text{opposite side}}{\text{hypotenuse}}$and $\cos\theta = \Large \frac{\text{adjacent}}{\text{hypotenuse}}$(Now, refer triangle PST and write down write $\sin\theta,\cos\theta$)
Now, simplify, substitue to express b and c only in terms of trig ratio, that is b=some tri ratio($\theta$) and c=some trig ratio($\theta$)
Similarly, for triangle PRQ Do you agree that