# Triangles with trigonometry

• Apr 18th 2010, 04:46 PM
bhuang
Triangles with trigonometry
If A is an obtuse angle in a triangle and sin A = 5/13, calculate the exact value of sin 2A.

I do not know how to go about this question. All I have done is found that the reference angle is about 22.6 degrees, but I have to find the exact value, how do I solve this?
• Apr 18th 2010, 04:49 PM
skeeter
Quote:

Originally Posted by bhuang
If A is an obtuse angle in a triangle and sin A = 5/13, calculate the exact value of sin 2A.

I do not know how to go about this question. All I have done is found that the reference angle is about 22.6 degrees, but I have to find the exact value, how do I solve this?

since $\displaystyle A$ is obtuse, $\displaystyle \cos{A} = -\frac{12}{13}$

$\displaystyle \sin(2A) = 2\sin{A}\cos{A}$
• Apr 18th 2010, 05:20 PM
bhuang
how did you get the ratio for cosine?
• Apr 18th 2010, 05:39 PM
skeeter
Quote:

Originally Posted by bhuang
how did you get the ratio for cosine?

I sketched a reference triangle in quad II ...

since $\displaystyle \sin{A} = \frac{5}{13}$ , opposite side = 5 , hypotenuse = 13

using Pythagoras ... adjacent side = -12

$\displaystyle \cos{A} = -\frac{12}{13}$