Andrew claims that a wooden bookend in the shape of a 45°- 45°- 90° right triangle has side lengths of 5 in., 5 in., and 8 in. Is he correct? If so, show the work and if not, show why not.
See my answer below.
To determine if Andrew is correct, we need to verify if the side lengths he provided form a 45°-45°-90° right triangle. In a 45°-45°-90° triangle, the two legs (the sides adjacent to the 45° angles) are congruent, and the hypotenuse (the side opposite the right angle) is √2 times the length of one of the legs.
According to Andrew, the side lengths of the triangle are 5 in., 5 in., and 8 in. Let's check if these dimensions satisfy the conditions for a 45°-45°-90° triangle:
1. Check if the two legs are congruent:
The given side lengths are 5 in. and 5 in., which are indeed equal. So, the first condition is satisfied.
2. Check if the hypotenuse is √2 times the length of one of the legs:
The length of one leg is 5 in. Therefore, the expected length of the hypotenuse based on the formula is √2 * 5 ≈ 7.071 in.
However, Andrew claims the length of the hypotenuse is 8 in., not approximately 7.071 in. This discrepancy tells us that the side lengths provided by Andrew do not form a 45°-45°-90° triangle.
Therefore, Andrew is not correct, as the side lengths he provided do not satisfy the conditions of a 45°-45°-90° triangle.