Question

find the measure of angle c.
round to the nearest tenth.

Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$. Here, $a = 15$, $A=70^{\circ}$, $c = 14$. So, $\frac{15}{\sin70^{\circ}}=\frac{14}{\sin C}$.

Step2: Solve for $\sin C$

Cross - multiply: $15\sin C=14\sin70^{\circ}$. Then $\sin C=\frac{14\sin70^{\circ}}{15}$.
Since $\sin70^{\circ}\approx0.9397$, we have $\sin C=\frac{14\times0.9397}{15}\approx\frac{13.1558}{15}\approx0.877$.

Step3: Find the measure of angle $C$

Using the inverse - sine function, $C=\sin^{-1}(0.877)$. So, $C\approx61.3^{\circ}$.

Answer:

$61.3$