About this video
This geometry lesson finds the tangent of angle R in a right triangle by using the similar triangle LMN. Tangent is opposite over adjacent, and corresponding sides of similar triangles keep the same ratio, so tangent R equals LM over LN. With LM = 4 and LN = 3, the answer is 4/3.
You'll be able to
- state tangent as opposite over adjacent for a right triangle.
- use corresponding sides of similar triangles to find a ratio.
- compute a trigonometric ratio from given side lengths.
Key words
- Tangent
- In a right triangle, the ratio of the opposite side to the adjacent side for an angle.
- Similar triangles
- Triangles with equal angles whose corresponding sides are in the same ratio.
- Corresponding sides
- Sides in the same relative position in two similar triangles.
- SOH-CAH-TOA
- A memory aid for sine, cosine and tangent as opposite or adjacent over hypotenuse or adjacent.
Transcript
- [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.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.