Question

Find the measure of angle y. Round your answer to the nearest hundredth. Right triangle

Answer 1

The measure of angle y is 35.68 degrees

Solution:

Given that,

hypotenuse 12

Opposite 7

Find the measure of angle y

y is unknown and is between the hypotenuse and adjacent side

The figure is attached below

In a right triangle, the sine of the angle is the ratio of the side opposite to the angle to the hypotenuse

Therefore,

$sin\ y = \frac{opposite}{hypotenuse}\\\\sin\ y = \frac{7}{12}\\\\sin\ y = 0.5833\\\\y = sin^{-1}\ 0.5833\\\\Use\ arcsin\ calculator\\\\y = 35.6829 \\\\y \approx 35.68$

Thus measure of angle y is 35.68 degrees