# Thread: find the angle with the greek letter

1. ## 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

2. Hello the kopite
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
OK, so now carry on:

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

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

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

$\Rightarrow \theta = 41.4^o$

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