Question

In triangle RST , cos R = 3/5 . What is sin T ?

Answer 1

Given:

`\cos R=(3)/(5)`

The cosine of angle R can be deffined as:

`\cos R=(adjcent)/(hypotenuse)`

Then:

`(adjacent)/(hypotenuse)=(3)/(5)`

adjacent leg for angle R is side RS

`\begin{gathered} (RS)/(15)=(3)/(5) \\ \\ \end{gathered}`

Use the equation above to find RS:

`\begin{gathered} RS=15*(3)/(5) \\ \\ RS=(45)/(5) \\ \\ RS=9 \end{gathered}`

Sine of angle T is:

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

Use the given data and the length of RS (opposite) to find the sinT:

`\begin{gathered} \sin T=(9)/(15) \\ \\ Simplify: \\ \sin T=(3)/(5) \end{gathered}`Then, the sine of T is 3/5