If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Trigonometry

### Course: Trigonometry>Unit 1

Lesson 5: Sine and cosine of complementary angles

# 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?

• 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
• does sohcahtoa only apply to right triangles?
• sohcahtoa can be only applied in right angled triangles.
• 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.
• 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.
• 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, the middle letter in that notation is the referenced angle by convention :).
<ABC and <CBA both reference the same angle.
• Where do we use sin cos tan in real life
• every time you use your GPS system to get somewhere, builders and surveyors, sailing, etc.