Find the measure of angle y. Round your answer to the nearest hundredth. (please type the numerical answer only) (4 points)

Question

A right triangle is shown with one leg measuring 7, and the hypotenuse is labeled 12. An angle across from the leg measuring 7 is marked y degrees.

Answer 1

To find angle y in the right triangle, we can use the sine function, which relates the opposite side to the hypotenuse. In this case:

\[ \sin(y) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{7}{12} \]

Now, we calculate angle y:

\[ y = \arcsin\left(\frac{7}{12}\right) \]

Let's calculate it using a calculator:

\[ y \approx \arcsin(0.5833) \approx 35.00 \]

So, rounding to the nearest hundredth, the answer is:

35.00