1
$\begingroup$

I have a triangle with

Side A = 2 Side B = 6

Angle c (angle opposite Side C) = 105°

I want to find side C

My first though was to use the SOH CAH TOA rule

In this case we have the adjacent and hypotenuse of angle c so I use CAH (cosθ = A/H)

Because 105° is in the 2nd quadrant it will be -cos

So -cos 105° = 2/C

Therefore C = 2/-cos 105°

        = 7.73

I thought this was the correct way to do it because that's all we have been learning in maths.

But in physics we are taught to use C = √(A²+B² - 2ABcosθ) which gives a different answer.

So which do I use/which is more accurate?

$\endgroup$
  • $\begingroup$ First rule doesn't apply. This is not a right triangle. Chris is correct. $\endgroup$ – JoeTaxpayer Aug 29 '13 at 2:17
  • 1
    $\begingroup$ Use the law of cosines... SOH CAH TOA requires a right triangle $\endgroup$ – Eleven-Eleven Aug 29 '13 at 2:19
2
$\begingroup$

Use the Cosine Law: $$c^2=a^2+b^2-2ab\cos(\angle C).\tag{1}$$ You know that $a=6$, so $b=3$, so now we know all the items on the right-hand side of (1).

Remark: The SOH CAH TOA stuff is for right-angled triangles. Our triangle is definitely not right-angled, since one of its angles is $105^\circ$.

Note that the Cosine Law is a generalization of the Pythagorean Theorem. If $\angle C=90^\circ$, then $\cos(\angle C)=0$, and the Cosine Law (1) becomes the familiar $c^2=a^2+b^2$.

$\endgroup$
0
$\begingroup$

Your angle is $105$ so the sohcahtoa rule doesn't apply. The law of cosines or the law of sines are for all triangles.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.