# How do you determine the number of possible triangles and find the measure of the three angles given PQ=12, PR=15, mangleR=100?

Feb 26, 2018

No solution is possible with the given SSA measurements.

#### Explanation:

$r = 12 , \hat{R} = 100 , q = 15$

Since one angle is obtuse, only one solution is possible with the measurements given.

$\sin Q = \frac{\sin R \cdot q}{r} = \frac{\sin 100 \cdot 15}{12}$

However, side q is greater than r. Therefore $\hat{Q}$ must be greater than $\hat{R}$. As $\hat{R}$ is already obtuse, no two obtuse angles exist in a triangle. Hence, no solution is possible with the given SSA measurements.