Right triangle trigonometry — Basic example

- [Instructor] In the figure above, triangle LMN is similar to triangle PQR. What is the value of tangent of angle R? So pause this video and see if you can figure this out before we do this together. All right, we wanna figure out the tangent of this angle right over here. Now, you might remember from basic trigonometry that tangent is opposite over adjacent. You might be familiar with soh cah toa. If you aren't, I encourage you to review all of the trigonometry on Khan Academy, especially the basic right triangle trigonometry. But this tells us that sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. So tangent of R is going to be equal to the length of the opposite side over the adjacent side. And we could also write this as QP over PR. Now, they don't give us any numbers here, but they do tell us that this right triangle is similar to this left triangle. And what we know about similar triangles is the ratio between corresponding sides is always the same. So QP, this side right over here, corresponds to ML right over here. So that's QP. And PR corresponds to LN right over here. So this is all going to be equal to the same thing as the ratio of LM, LM, to LN, to LN. And, of course, LM has a length 4, so this is 4. And LN has length 3. So the tangent of R is going to be equal to 4/3, and we're done.