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Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale.
Right triangle with hypotenuse labeled 11 and one leg labeled x. The angle between the leg labeled x and the hypotenuse is equal to 22 degrees.
To find the value of x in this right triangle, we can use the sine function, which relates the angle of a right triangle to the ratio of the length of the opposite side to the hypotenuse.
In this case, we know that the angle opposite side x has a length of 11, and the angle between x and the hypotenuse is 22 degrees.
We can therefore set up the equation:
sin(22 degrees) = x/11
To solve for x, we can multiply both sides of the equation by 11:
11 * sin(22 degrees) = x
Using a calculator, we find that sin(22 degrees) is approximately 0.3746:
11 * 0.3746 ≈ 4.12
Therefore, the value of x rounded to the nearest tenth is approximately 4.1.