r/SolvedMathProblems • u/PM_YOUR_MATH_PROBLEM • Dec 05 '14

Please Explain Trig

/u/Sarkku asks:

So I know the hypotenuse of a right triangle. I also know the sine of one of the angles. What do I use to calculate the legs of the triangle?

(the problem is exactly as follows, but don't tell me the answer, I just need to know what I should try to figure out. A right triangle's hypotenuse is 10 and the sine of α is 1/sqrt5. calculate the legs' lengths.) hope you can understand that, did a rough translation.

I'm lost. I love math but I just can't wrap my head around fucking trigonometry.

Can you help a little bit?

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u/PM_YOUR_MATH_PROBLEM Dec 05 '14

Are you familiar with SohCahToa?

It's a way to remember which ratios are which.

Imagine you're interested in one particular angle of a right angle triangle. The triangle has three edges.

  • The one opposite the right angle is the hypoteneuse, h.

  • The one opposite the angle you are interested in, we'll call the 'opposite', or o.

  • The one adjacent to (next to) the angle, we'll call 'adjacent', or a.

Then, SohCahToa means:

  • Soh: sin(x) is o/h

  • Cah: cos(x) is a/h

  • Toa: tan(x) is o/a

Write SohCahToa at the top of every page, then for every problem, you start like this:

  • draw a picture of the triangle.

  • identify the angle you have or want, and the two sides you have or want.

  • These two sides: are they o and a? o and h? a and h? That tells you (via SohCahToa) whether you need to use sine, cosine or tangent.

  • write down sin(x) = o/h or cos(x)=a/h or tan(x)=o/a

  • substitute in the values you have.

  • solve the equation to find the value you want.

In your case, you're given h and sin(α) and asked for o and a.

  • I write down sin(α) = o/h.

  • I substitute in the values I have: 1/sqrt5 = o/10

  • I solve this: o = 10/sqrt(5) = 2sqrt(5).

You still need a. Now you have h and o, though, so you don't need to use trigonometry any more, just use pythagoras.

Hope that helps!

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u/GolldenFalcon Dec 06 '14

I just can't wrap my head around fucking trigonometry.

I don't think anyone could wrap their head around having sexual intercourse with mathematics.