Final answer:
The length of the side opposite to the given angle is 5.02, the length of the side adjacent to the given angle is 20.75, and the other acute angle is 7π/8 (in radians).
Step-by-step explanation:
To solve the right angle triangle, let's find the length of the side opposite to the given angle (opposite side) and the length of the side adjacent to the given angle (adjacent side). We can use the Pythagorean theorem to find these lengths. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, using the equation c^2 = a^2 + b^2, where c represents the hypotenuse, a represents the opposite side, and b represents the adjacent side, we can solve for a and b. Given that the hypotenuse c is 41.5 and the angle A is π/8:
a = c*sin(A) = 41.5*sin(π/8) = 5.02 (rounded to two decimal places)
b = c*cos(A) = 41.5*cos(π/8) = 20.75 (rounded to two decimal places)
The other acute angle, denoted as B, can be found using the formula B = π/2 - A = π/2 - π/8 = 7π/8 (in radians)