Final answer:
Using the Pythagorean theorem and trigonometric ratios, one can find the length of the other leg and the hypotenuse of the right triangle when one leg and an acute angle are known.
Step-by-step explanation:
The student's question relates to the Pythagorean theorem and its application in determining various lengths in a right triangle. Since one leg of the triangle is 8 cm and the angle opposite this leg is 50 degrees, we can use trigonometric ratios to find the length of the other leg and the hypotenuse. To find the length of the other leg (let's call it b), we can use the tangent function (tan) because it relates the opposite side to the adjacent side in a right triangle:
tan(50°) = opposite/adjacent
Finding the length of the hypotenuse (let's call it c) involves the Pythagorean theorem:
a² + b² = c²
By plugging in the known values and solving, one can find the measure of the unknown sides.