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### Course: Geometry (all content)>Unit 13

Lesson 6: Trigonometric ratios and similarity

# Trig challenge problem: trig values & side ratios

Sal is given a diagram with multiple right triangles and is asked to match different expressions with different trig values. Created by Sal Khan.

## Want to join the conversation?

• does sohcahtoa only apply to right triangles?
• sohcahtoa can be only applied in right angled triangles.
• I'm confused. How is cos(<DEC) equal to sin(41°)?
• Cos(<DEC)=Sin(41˚) because cos (<DEC)=adj/hyp which is also = sin(41˚) = opp/hyp
• Where could trig be used in the real world?
• It's used in a plethora of occupations such as architecture, engineering, computer programming, graphical design, manufacturing, construction, and much more. Trig serves as a huge part of the foundations of Geometry, so basically anything in life that involves shapes finds uses for Trigonometry.
• Around , how do you know the angle he marked was the one you were supposed to take the cosine of? Because the of the order of the letters?
• Yes the order of the letters mean that the vertex of the angle will be the central letter, so you can trace the letters in order to create an angle.
• Am I correct in assuming that if we have a right triangle where the other two angles are x and y then we will always get cos(x) = sin(y) and cos(y) = sin(x)?
• Yes! Because cos is A/H,sin is O/H and if θ is an angle and θ+90 is another,in a right triangle ,then the side opposite of θ will be adjacent to θ+90,and the side opposite of θ+90 will be adjacent to θ.
• Am I capable of determining the measure of each angle in the video without having to do so much work?
• Hi Jorge,

Take heart. With practice you will be able to solve these problems very quickly. If it helps consider that today's work is the foundation for the future. Many interesting fields of study depend on trigonometry.

Regards,

APD
• Forgive me if this was covered, but I don't remember it actually getting mentioned. So to clarify, when Sal takes the cos(∠DEC), I notice that he used the value of angle E. Is there a notational standard that dictates, that in a case like the one above, the reference angle will be the middle angle. I notice he also did this in the problem sin(∠CDA), where he used D as his reference. Thanks in advance for clarifying this. :)
• Yes when you label an angle with three points (often necessary when multiple triangles/angles are present), then the middle point always indicates the vertex of the angle. So ∠CDA is not the same as angle ∠DAC.
Good observation and conclusion.
(1 vote)
• Wait, when asked for the sin/cos/tan of a whole triangle, like <DEC or <CDA, how do you figure out what the adjacent vs opposite is, coz there doesn't seem to be any information that determines which angle's perspective you're evaluating from..?

I kinda got the feeling that he's just arbritrarily deciding to evaluate from the perspective of whichever ever angle's measurement is given, like with <DEC the only given measure is 41deg and with <CDA the one given is 30deg.

But that wouldn't make sense in the larger world so I'm assuming there's something I'm missing lol.
• Nevermind, I read some more comments and learned that the reference angle is whatever letter is in the middle, so for <DEC it's E and for <CDA it's D.