Answer:
Your answer is: No, it is not a right triangle
Explanation:
We can use the Pythagorean theorem to determine if a triangle is a right triangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's label the sides of the triangle:
Side A = 72 miles
Side B = 85 miles
Side C = 36 miles
To check if it's a right triangle, we can compare the lengths of the sides using the Pythagorean theorem:
1. Calculate the squares of the lengths of Side A and Side B:
- A^2 = 72^2 = 5184
- B^2 = 85^2 = 7225
2. Calculate the square of the length of Side C:
- C^2 = 36^2 = 1296
3. Check if the sum of the squares of the two shorter sides (A^2 + B^2) is equal to the square of the longest side (C^2):
- A^2 + B^2 = 5184 + 7225 = 12409
- C^2 = 1296
Since A^2 + B^2 is not equal to C^2 (12409 ≠ 1296), we can conclude that the given triangle is not a right triangle.