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?

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- May 4th 2008, 11:25 AMemmahlavSolving triangle ABC using given measurements
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? - May 4th 2008, 11:29 AMJason Holm
Well if it's a right triangle, one angle is 90. You said another is 40, and all three angles of a triangle should equal 180. Is side A the hypotenuse or one of the other sides?

- May 4th 2008, 11:32 AMemmahlav
yeah so A=50 B=40 C=90

a is not the hypotenuse, c is - May 4th 2008, 11:48 AMJason Holm
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

- Use the
- May 4th 2008, 11:49 AMJason Holm
The

**Law of Sines**defines the relationship between the sine of any angle in a triangle and the side opposite it. The formula is:*a/sinA = b/sinB = c/sinC* - Jun 2nd 2008, 02:22 AMchelsealover25
lengths - a = 14cm

- b = 16.68cm

-c = 21.78cm

angles - A = 50

- B = 40

- C = 90 - Jun 2nd 2008, 07:37 AMmasters
- Jun 2nd 2008, 07:40 AMtopsquark
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