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### Course: Digital SAT Math > Unit 13

Lesson 3: Right triangle trigonometry: advanced# Right triangle trigonometry — Basic example

Watch Sal work through a basic Right triangle trigonometry problem.

## Want to join the conversation?

- Are we allowed to draw visual aid on the SAT test?(17 votes)
- Pretty sure you can draw on the booklet with the problems on it. Not the answer sheet though.(49 votes)

- Wouldn't it be easier (at4:40) to prove that quadrilateral ACDB is a parallelogram?

Since the sides are parallel it is easy to prove and then you know that the opposite angles are congruent.(25 votes) - the law of sine and cosine formula is another way to solve it(12 votes)
- No, they can only be applied in non-right angle triangles(2 votes)

- All I did was cos(70) = x / 8.9 and I got the right answer. Did I simply get lucky or did I actually solve it correctly?(3 votes)
- Yes that is the correct beginning. To isolate for x, you multiply both sides by 8.9, so

x = 8.9 ∙ cos(70)

x ≈ 8.9 (0.342)

x ≈ 3.04

Of course you need to know from geometry that`the side you solved for will be congruent to the side they are asking for`

. About half the video seems to be about proving that CD ≅ AB, the side they are asking for, by proving that the two triangles are congruent and that those two sides are corresponding sides of the two triangles.(10 votes)

- in which sections are we allowed to use a calculator(4 votes)
- There are two math sections, the first one is 20 questions and you will not be able to use the calculator, the second section is devised of 38 questions and you will be able to use a calculator. Just for reference the first section is mostly just math theory, so if you know the basic principles taught in Pre-Algebra, Algebra 1 and 2, and some geometry you shouldn't need a calculator. Hope this helps!(7 votes)

- Hi guys...do we have a Nigerian in the house...I feel pretty lonely here...?(7 votes)
- better than SOH CAH TOA

remember this sentence

*S*ome People Have *C*urly Brown Hair *T*hrough Proper Brushing.

Sine=S=P/H

COSINE=C=B/H

TAN=T=P/B

> P=Perpendicular

B=Base

H=Hypotenuse(5 votes) - I like to SOHC AH TOA(5 votes)
- I heard the new SAT can both be taken on the computer or sheet and we get to choose. If we take it on the computer would we still be given scratch papers?(3 votes)
- I think you will be given about 3 pages and a graph paper. Although if you wanted to make sure I would take it on paper but if you're not comfortable with paper I would ask a teacher or guidance counsel(5 votes)

- The pain when he wrote LM/LN instead of 4/3.(4 votes)

## Video 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.