Question

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Find the value of x. Round to the nearest degree.
A right triangle is drawn with an angle that is labeled x degrees. The leg opposite of the labeled angle is 7. The hypotenuse is 9.

Answer 1

To find the value of x, we can use the sine function. The sine of an angle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we have:

sin(x) = opposite/hypotenuse

sin(x) = 7/9

To solve for x, we need to take the inverse sine (also known as arcsine) of both sides of the equation:

x = sin^(-1)(7/9)

Using a calculator, we find that sin^(-1)(7/9) is approximately 49.27 degrees.

Therefore, x is approximately 49 degrees rounded to the nearest degree.