How do you determine the number of possible triangles and find the measure of the three angles given a=6, c=10, mangleA=45?

Mar 26, 2018

Since $\sin \theta$ can not have a value more than 1, $\left(\sin 90 = 1\right)$, no triangle is possible with the given measurements.

Explanation:

Given : $a = 6 , c = 10 , \hat{A} = {45}^{\circ}$

Applying the law of sines,

$\sin \frac{A}{a} = \sin \frac{B}{b} = \sin \frac{C}{c}$

sin C = (c * sin A) / a = (10 ^ sin 45) / 6 = 1.1785#

Since $\sin \theta$ can not have a value more than 1, $\left(\sin 90 = 1\right)$, no triangle is possible with the given measurements.