Final answer:
Using the Pythagorean theorem and the given information that the hypotenuse is four times the length of one leg, with the other leg being 1215 feet, the unknown leg length was found to be 313.5 feet and the hypotenuse length 1254 feet.
Step-by-step explanation:
To solve for the lengths of the leg and the hypotenuse of a right triangle when given one leg length, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two legs (a and b).
Given that the hypotenuse is four times the length of one leg and that the length of the other leg is 1215 feet, let's call the unknown leg length 'x'. So the hypotenuse is '4x'. The Pythagorean theorem gives us:
x² + (1215)² = (4x)²
Now we can solve for x:
- x² + 1476225 = 16x²
- 15x² = 1476225
- x² = 98415
- x = √98415
- x = 313.5 feet (the length of the leg)
Therefore, the hypotenuse is:
- 4x = 4(313.5 feet) = 1254 feet
Hence, the length of the unknown leg is 313.5 feet and the length of the hypotenuse is 1254 feet.