Question

Question50 in.eThe figure above shows a right triangle with dimensions in inches. If O = 48°, what is the length of y to the nearest inch?

Answer 1

Remember the definition of the sine trigonometric relation in a right triangle:

$\sin \theta=\frac{\text{Side opposite to }\theta\text{ }}{\text{Hypotenuse}}$

In this case, we have:

$\sin (48º)=\frac{y}{50in}$

Isolate y and use a calculator to find its numerical value to the nearest inch:

$\begin{gathered} y=(50in)\times\sin (48º) \\ =37.15724127\ldots in \\ \approx37in \end{gathered}$

Therefore, the length of y to the nearest inch, is 37.