Question

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

Answer 1

Given:

$\cos R=\frac{3}{5}$

The cosine of angle R can be deffined as:

$\cos R=\frac{adjcent}{hypotenuse}$

Then:

$\frac{adjacent}{hypotenuse}=\frac{3}{5}$

adjacent leg for angle R is side RS

$\begin{gathered} \frac{RS}{15}=\frac{3}{5} \\ \\ \end{gathered}$

Use the equation above to find RS:

$\begin{gathered} RS=15*\frac{3}{5} \\ \\ RS=\frac{45}{5} \\ \\ RS=9 \end{gathered}$

Sine of angle T is:

$\sin T=\frac{opposite}{hypotenuse}$

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

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