find the measure of angle c.\nround to the nearest tenth.

Explanation:

Step1: Use 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), (c = 14), and (A=70^{\circ}). 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), (\sin C=\frac{14\times0.9397}{15}\approx\frac{13.1558}{15}\approx0.877).

Step3: Find the measure of angle (C)

(C=\sin^{- 1}(0.877)\approx61.3^{\circ})

Answer:

(61.3)