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√(5) \\ AC=6√(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=(3√(5))/(6√(7)) \\ sinC=(3√(5))/(6√(7))*(√(7))/(√(7)) \\ sinC=(3√(35))/(6*7) \\ sinC=(3√(35))/(42) \end{gathered}`
`\begin{gathered} sinC=(√(35))/(14) \\ C=sin^(-1)((√(35))/(14)) \end{gathered}`