# find the angle with the greek letter

• May 19th 2009, 10:10 PM
the kopite
find the angle with the greek letter
in the triangle ABC, AC=3, BC=2, angleBAC=theta and angleABC=2theta
calculate the value of theta to the nearest tenth of a degree.
i think i'm complicating this thing for myself because i cant get farther than 2 x sin2theta = 3 x sintheta (Punch)
• May 19th 2009, 10:25 PM
Hello the kopite
Quote:

Originally Posted by the kopite
in the triangle ABC, AC=3, BC=2, angleBAC=theta and angleABC=2theta
calculate the value of theta to the nearest tenth of a degree.
i think i'm complicating this thing for myself because i cant get farther than 2 x sin2theta = 3 x sintheta (Punch)

OK, so now carry on:

$\displaystyle 2\sin2\theta = 3\sin\theta$

$\displaystyle \Rightarrow 4\sin\theta\cos\theta = 3 \sin\theta$

$\displaystyle \Rightarrow \sin\theta = 0$ or $\displaystyle \cos\theta = \tfrac34$

$\displaystyle \Rightarrow \theta = 41.4^o$

$\displaystyle sin 2\theta = 2sin \theta cos\theta$