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.
Using trigonometry, we can set up the equation:
sin(22°) = x/11
Multiplying both sides by 11, we get:
x = 11*sin(22°)
Using a calculator, we find:
x ≈ 4.2
Therefore, the value of x rounded to the nearest tenth is 4.2.
To find the value of x in the right triangle, we can use the trigonometric function cosine (cos).
The cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. In this case, the adjacent side is x and the hypotenuse is 11.
Using the formula: cos(angle) = adjacent / hypotenuse
We can plug in the known values: cos(22 degrees) = x / 11
To find the value of x, we can rearrange the equation and solve for x:
x = cos(22 degrees) * 11
Now, we can use a calculator to find the cosine of 22 degrees and multiply it by 11.
cos(22 degrees) is approximately 0.927 (rounded to three decimal places)
x = 0.927 * 11
Using a calculator, we find that x is approximately 10.201 (rounded to the nearest tenth).
Therefore, the value of x, rounded to the nearest tenth, is 10.2.
To find the value of x, we can use trigonometric functions. Since we know the angle between the leg labeled x and the hypotenuse is 22 degrees, we can use the sine function.
sin(22°) = opposite / hypotenuse
We know the hypotenuse is 11 and we want to find the length of the leg labeled x (opposite side). Rearranging the formula, we can solve for x:
x = sin(22°) * hypotenuse
Substituting the given values:
x = sin(22°) * 11
Using a calculator, we can evaluate sin(22°):
sin(22°) ≈ 0.3746
Now, we can find the value of x:
x ≈ 0.3746 * 11 ≈ 4.12
Rounded to the nearest tenth, x is approximately 4.1.