Solving Soh Cah Toa: Understand & Find Angles and Sides

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Discussion Overview

The discussion revolves around understanding and applying the trigonometric ratios of sine, cosine, and tangent in the context of right triangles. Participants explore how to find angles and sides using these ratios, addressing confusion and seeking clarification on specific examples.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about how to use the sine, cosine, and tangent ratios to find angles and sides in right triangles.
  • Another suggests drawing a right triangle and labeling the sides and angles to clarify the relationships, emphasizing the importance of specifying which angle is being referred to.
  • A participant provides an example involving a right triangle with a 20-degree angle and a hypotenuse of 6 cm, questioning how to calculate the other sides.
  • In response, another participant calculates the opposite side using the formula x = 6 * Sin20 and the adjacent side using y = 6 * Cos20, while also referencing the Pythagorean theorem.
  • There is confusion regarding a statement about sine that one participant acknowledges as unclear, leading to a recommendation to disregard it.
  • Another participant mentions the properties of 30-60-90 triangles, suggesting a specific relationship between the sides in such triangles.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and confusion regarding the application of trigonometric ratios. There is no consensus on the best approach to clarify these concepts, and multiple viewpoints on how to interpret the sine function and its application are present.

Contextual Notes

Some participants reference specific triangles and relationships without fully resolving the underlying confusion about trigonometric functions and their applications. The discussion includes unresolved mathematical steps and assumptions about prior knowledge.

Who May Find This Useful

This discussion may be useful for students struggling with the application of trigonometric ratios in right triangles, particularly those seeking clarification on how to find angles and sides using sine, cosine, and tangent.

havechanged
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I understand that Sin is Opposite over the Hypotenuse, Cosine is Adjacent over Hypotenue, and Tangent is Opposite over the Adjacent. But I don't know how to use it. Sin has its own equation, as does Tangent...I am just confused. What do I do to find a specific angle? What about a certain side?

Thanks!

P.S I have done Soh Cah Toa during previous school years, but I never understood!
 
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Then all I can recommend is that you draw a right triangle, label the sides and angles, stare at it for a while and THINK!

It might help if you specified on your triangle, which angle you are talking about "sin is opposite over hypotenuse" is non-sense until you specify the angle! Never say "sin". It is always sin OF A PARTICULAR ANGLE.
 
Ok...here could be an example:

One angle of a right triangle is 20 degress. The length of the hypotenuse is 6 cm. How would I get the other two sides?

For the opposite side, would it be something like Sin20 is x/6?

It just doesn't make sense...What about the whole Sin is the square root of a plus b times a and b or something like that?

Thanks!
 
So you have

x= 6* Sin20 for the opposite side,

the adjacent side would be

y = 6* Cos20

I am not sure what your last comment is about, are you referring to the Pythagorean theorem.

a2+ b2= c2?
 
Thanks for the reply.

No, it wasn't the pathagorem theorum. I don't know what it was.

Thanks again!
 
"What about the whole Sin is the square root of a plus b times a and b or something like that? "

Now THAT'S the part that doesn't make sense! I recommend you erase that from your mind immediately!
 
Ok, I will. If I do find out what I was thinking of, I'll post it!
 
pay attention in class

your thinkin of 30 60 90 triangles. that's where the side across from the right angle ( hypotenuse) equals 2x. the side across from the 30 degree angle equals x and the side across from the 60 degree angle is x times the squareroot of 3
 

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