Question

Suppose you have a right triangle called AABC where B is the right angle. If AB = 3√5and AC = 6√7, which can be used to find mzC?

Answer 1

Given: The right triangle ABC

$\begin{gathered} \angle B=90^0 \\ AB=3\sqrt{5} \\ AC=6\sqrt{7} \end{gathered}$

To Determine: The measure of angle C

Solution

The diagram below represents the given information

Using trigonometry

Apply trigonometric ratios

$\begin{gathered} sinC=\frac{3\sqrt{5}}{6\sqrt{7}} \\ sinC=\frac{3\sqrt{5}}{6\sqrt{7}}\times\frac{\sqrt{7}}{\sqrt{7}} \\ sinC=\frac{3\sqrt{35}}{6\times7} \\ sinC=\frac{3\sqrt{35}}{42} \end{gathered}$$\begin{gathered} sinC=\frac{\sqrt{35}}{14} \\ C=sin^{-1}(\frac{\sqrt{35}}{14}) \end{gathered}$