Question

Find the length of AC and the measures of a and 0

Answer 1

AC = 3√ 17

α = 75.96°

Θ = 14.04°

Explanation:

We can calculate the length of side AC by means of the Pythagorean theorem, just like this:

`\begin{gathered} c^2=a^2+b^2 \\ \text{ in this case:} \\ (AC)^2=3^2+12^2 \\ (AC)^2=9+144 \\ AC=\sqrt[]{153} \\ AC=3\sqrt[]{17} \end{gathered}`

We can calculate the angles by applying the following trigonometric ratios:

`\begin{gathered} \sin \alpha=\frac{12}{3\sqrt[]{17}} \\ \alpha=\arcsin \mleft((12)/(3√(17))\mright) \\ \alpha=75.96 \\ \\ \sin \theta=\frac{3}{3\sqrt[]{17}} \\ \theta=\arcsin \mleft((3)/(3√(17))\mright) \\ \theta=14.04 \end{gathered}`