Answer:
Explanation:
To solve for x in a triangle where one angle is 32 degrees and the opposite leg has a length of 20, you can use the trigonometric function tangent (tan).
The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, you know the angle (32 degrees) and the length of the side opposite the angle (20). You want to find the length of the side adjacent to the angle, which is represented by x.
So, you can set up the following equation:
tan(32 degrees) = Opposite / Adjacent
tan(32 degrees) = 20 / x
Now, you can solve for x by isolating it:
x = 20 / tan(32 degrees)
Using a calculator:
x ≈ 20 / 0.62487
x ≈ 31.99
Rounded to two decimal places, x is approximately 31.99.