In right triangle $ABC$ with $\angle B = 90^\circ$, we have $2\sin A = 3\cos A$. What is $\tan A$?

ellapow Apr 26, 2021

#1**0 **

From SOHCAHTOA, we conclude that sin A = BC/AC and cos A = AB/AC. We have BC/AC=2AB/AC, or BC=2AB. You want tan A, which is BC/AB by SOHCAHTOA. But you have BC=2AB, so BC/AB=2, which is your answer.

XxAngelGirlxX Apr 26, 2021

#2**+2 **

One of the trig identities state that \(\tan A = \frac{\sin A}{\cos A}\) (you could just prove it by using sohcahtoa), so that's what we need to solve for. To do that, divide both sides by cos A and then by 2 to get:

\(\frac{\sin A}{\cos A} = \boxed{\frac{3}{2}}\), which is our final answer.

textot
Apr 26, 2021