Question

Hi, can you help me to solve this exercise, please!!

Answer 1

Given the Right Triangle BCD, you know that:

`\begin{gathered} BD=8 \\ m\angle BCD=63\degree \end{gathered}`

Then, you can use the following Trigonometric Function in order to find the length of the side CD:

`\sin \beta=(opposite)/(hypotenuse)`

In this case:

`\begin{gathered} \beta=63\degree \\ opposite=BD=8 \\ hypotenuse=CD \end{gathered}`

Therefore, substituting values and solving for CD, you get:

`\begin{gathered} \sin (63\degree)=(8)/(CD) \\ \\ CD\cdot\sin (63\degree)=8 \end{gathered}`
`\begin{gathered} CD=(8)/(\sin(63\degree)) \\ \\ CD\approx9.0 \end{gathered}`

Hence, the answer is:

`CD=9.0`