Question

question 10 (fill - the - blank worth 4 points)
(05.03 mc)
find the measure of angle y. round your answer to the nearest hundredth. (please type the numerical answer only)
numerical answers expected!
answer for blank 1

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine of an angle \(y\) is given by \(\sin y=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the side opposite to angle \(y\) is \(7\) and the hypotenuse is \(12\). So, \(\sin y=\frac{7}{12}\).

Step2: Solve for \(y\)

To find \(y\), we use the inverse sine function \(y = \sin^{-1}(\frac{7}{12})\). Using a calculator, \(y=\sin^{-1}( \frac{7}{12})\approx35.69\) (rounded to the nearest hundredth).

Answer:

\(35.69\)