Final answer:
In a right triangle, the length of the hypotenuse is given as 12. Using the Pythagorean theorem, we can find the relationship between the lengths of the sides a and b. The equation a^2 + b^2 = c^2 can be used to solve for the lengths of a and b.
Step-by-step explanation:
The length of the hypotenuse is 12. Let's label the sides of the right triangle as follows: a is the length of the side opposite the 10° angle, b is the length of the side opposite angle b, and c is the length of the hypotenuse.
According to the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse, we have the equation: a² + b² = c².
Since we know that the length of the hypotenuse is 12, we can substitute this value into the equation to find the lengths of sides a and b.
12² = a² + b²
144 = a² + b²
We cannot determine the exact values of a and b without more information, but we can say that they satisfy the equation a² + b² = 144.