# How do you determine the number of possible triangles and find the measure of the three angles given a=8, b=10, mangleA=45?

Feb 26, 2018

Solution (1) $\hat{.} = {45}^{\circ} , \hat{B} = {62.12}^{\circ} , \hat{C} = {72.88}^{\circ}$

Solution (2) $\hat{.} = {45}^{\circ} , \hat{B} = {117.88}^{\circ} , \hat{C} = {17.12}^{\circ}$

#### Explanation:

$\hat{A} = 45 , a = 8 , b = 10$

Applying law of sines,

$\sin B = \frac{\sin A \cdot b}{a} = \frac{\sin 45 \cdot 10}{8} \approx 0.8839$

$\hat{B} = {\sin}^{-} 1 0.8839 \approx 62.12$

$\hat{C} = 180 - 45 - 62.12 = {72.88}^{\circ}$

Since $\hat{A} + \hat{B} = 45 + 62.12 = 107.12$ is less than ${180}^{\circ}$, we will have one more solution.

Supplementary angle of $\hat{B} = 180 - 62.12 = {117.88}^{\circ}$

$\hat{C} = 180 - 117.88 - 45 = {17.12}^{\circ}$