these formulas only used for the right triangle?

Question

Can I use the following relationships to calculate the sides of the below triangle (in the picture)?

$tan5=\frac{AB}{6}$

$cos5=\frac{6}{AC}$

Can we use these formulas only for the right triangle? I heard that, but I'm not sure if I heard it right or not, if that's right, Why are these formulas used only for right triangles?

Answer 1

No you can't. The formulae

$$\tan(\theta) = \frac {\text{opposite}}{\text{adjacent}} \qquad \cos(\theta) = \frac {\text{adjacent}}{\text{hypotenuse}}$$

only apply when you have a right angle. In this case, angle $CBA$ is $120$ so these formulae don't apply.

The reason why it only applies to right angled triangles is simply because that is how the trigonometric functions are defined.

Answer 2

No you can't, because SOH CAH TOA is only valid for right angled triangles.

For this question, make use of the sine rule:

$$\frac{AB}{\sin (5)}=\frac{AC}{\sin (120)}=\frac{6}{\sin (\angle{BAC})}$$