Two artillery

Objective C we observe from two artillery observatories, A and B, which are 975 m apart. The size of the BAC angle is 63°, and the size of ABC is 48°. Calculate the distance of points A and C.

Correct answer:

AC =  776.1155 m

Step-by-step explanation:

$$\begin{gathered} AB=975\text{m} \\ \angle BAC=63{}^{\circ } \\ \angle ABC=48{}^{\circ } \\ \angle ACB=180-\angle BAC-\angle ABC=180-63-48=69{}^{\circ } \\ \sin ABC:\sin ACB=AC:AB \\ AC=AB\cdot \frac{\sin ABC}{\sin ACB}=AB\cdot \frac{\sin 48°}{\sin 69°}=975\cdot \frac{\sin 48°}{\sin 69°}=975\cdot \frac{0.743145}{0.93358}=776.115=776.1155\text{m} \end{gathered}$$

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