Final answer:
In an isosceles right triangle, the two acute angles are equal. Using the properties of right triangles, we can find the measure of each acute angle by finding the length of the hypotenuse and using trigonometric ratios. In this case, each acute angle measures 45 degrees.
Step-by-step explanation:
The front and back of the storage shed are shaped like isosceles right triangles. In an isosceles right triangle, the two acute angles are equal. Since the base of the triangle is 8 meters, we can use the properties of right triangles to find the measure of each acute angle.
Let's call the acute angle θ. In a right triangle, the hypotenuse is always the longest side, and the other two sides are the legs. In an isosceles right triangle, the two legs are equal in length. So, in this case, each leg has a length of 8 meters.
Using the Pythagorean theorem, we can find the length of the hypotenuse. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs.
Hypotenuse^2 = Leg^2 + Leg^2
Hypotenuse^2 = 8^2 + 8^2
Hypotenuse^2 = 64 + 64
Hypotenuse^2 = 128
Hypotenuse = sqrt(128)
Hypotenuse = 8*sqrt(2)
Now, we can find the value of the acute angle θ using trigonometric ratios. In this case, we can use the sine ratio. The sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse.
sin(θ) = Leg / Hypotenuse
sin(θ) = (8 / (8*sqrt(2)))
sin(θ) = 1 / sqrt(2)
sin(θ) = sqrt(2) / 2
Since θ is an acute angle, its value must be between 0 and 90 degrees. Using the inverse sine function, we can find the measure of θ:
θ = sin^(-1)(sqrt(2) / 2)
θ = 45 degrees
So, the measure of each acute angle in the isosceles right triangle is 45 degrees. Therefore, the correct option is B) 45 degrees.