I was not paying attention in class when this was taught and now I'm completely lost
right triangle ABC
B=40 degrees
side a=14
what do I do next?
Here's the steps, but I don' know offhand how to do each of them:
If you know two angles and any side:
- Use the Sum of the Angles with the two angles to find the third angle
- Use the Law of Sines and plug in the values for the two angles and the side
- Solve for the side
- Use the Law of Sines with an angle, the side opposite it, and the angle opposite the side you still don't know to find that side
You can use simple trigonometric definitions. No need to get fancy.
$\displaystyle cos(40^o) = \frac{14}{c} \implies c = 18.2757$
and
$\displaystyle tan(40^o) = \frac{b}{14} \implies b = 11.7474$
And you can check your answers using the Pythagorean Theorem: $\displaystyle 14^2 + b^2 = c^2$.
-Dan