Final answer:
To find the length of the longer leg of a right triangle, use the Pythagorean theorem by relating the lengths of the sides and the hypotenuse. In this case, use the cosine function to find the length of the longer leg.
Step-by-step explanation:
To find the length of the longer leg of a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Given that the length of the hypotenuse is 8 and the measure of an acute angle is 22 degrees, we can find the length of the longer leg as follows:
- Let x be the length of the longer leg.
- Using the cosine function, cos(22) = x/8.
- Solving for x, x = 8 * cos(22).
- Calculate x using a calculator, x ≈ 7.2526.
- Rounding x to the nearest unit, the length of the longer leg is 7 units.