Final answer:
The other acute angle in the right triangle is 40 degrees. The other leg length is 6 cm, obtained by applying the tangent function for the 50-degree angle. The hypotenuse is found to be 10 cm by using the Pythagorean theorem.
Step-by-step explanation:
The problem involves a right triangle where one leg length and one acute angle are given. To find the measure of the other acute angle, we take into account that the sum of the angles in any triangle is 180 degrees, and since one is a 90-degree angle (right triangle), we subtract the given 50-degree angle from the remaining 90 degrees (180-90-50). Hence, the other acute angle measures 40 degrees.
To find the lengths of the other leg and the hypotenuse, we can use trigonometric ratios and the Pythagorean theorem. For the other leg length (adjacent to the 50-degree angle), we can use the tangent function: tan(50 degrees) = opposite/adjacent, solving for the adjacent side length. To find the length of the hypotenuse, the Pythagorean theorem (a² + b² = c²) is used, where 'c' represents the hypotenuse and 'a' and 'b' are the legs of the triangle. Having one of the leg lengths (8 cm) and needing the hypotenuse, we can rewrite this equation as c = √(a² + b²).
After performing the relevant calculations and using a calculator to find the lengths, one can determine that the correct answer is, in fact, option a: Other acute angle = 40 degrees, other leg = 6 cm, hypotenuse = 10 cm.