# How do you determine the number of possible triangles and find the measure of the three angles given RS=3sqrt3, ST=3, mangleT=60?

Feb 26, 2018

Only one solution possible.

$\hat{R} = {30}^{\circ} , \hat{S} = {90}^{\circ} , \hat{T} = {60}^{\circ}$ are the measures of the three angles.

#### Explanation:

In Triangle RST. $\hat{T} = 60 , t = 3 \sqrt{3} , r = 3$

$\sin R = \frac{\sin T \cdot r}{t} = \frac{3 \cdot \sin 60}{3} \sqrt{3} = 0.5$

$\hat{R} = {\sin}^{-} 1 0.5 = {30}^{\circ}$

$\hat{S} = 180 - 30 - 60 = {90}^{\circ}$

It’s a right triangle with angles measuring ${30}^{\circ} , {60}^{\circ} , {90}^{\circ}$

Sin (180 - R) = sin (180 - 30) = 120^@#

As $\hat{T} + \hat{R} = 0 + 120 = {180}^{\circ}$, $\hat{R}$ as obtuse angle cannot form a triangle.