Final answer:
The missing length in the right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). In this case, we are given the lengths of one of the sides (a = 9mi) and the hypotenuse (c = 14mi), and we need to find the length of the other side (b). The length of the missing side is approximately 10.7mi.
Step-by-step explanation:
The missing length in the right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). In this case, we are given the lengths of one of the sides (a = 9mi) and the hypotenuse (c = 14mi), and we need to find the length of the other side (b). So, using the Pythagorean theorem, we have:
c = sqrt(a^2 + b^2)
14mi = sqrt((9mi)^2 + b^2)
Squaring both sides:
196mi^2 = (9mi)^2 + b^2
Subtracting (9mi)^2 from both sides:
196mi^2 - (9mi)^2 = b^2
Simplifying:
196mi^2 - 81mi^2 = b^2
b^2 = 115mi^2
Taking the square root of both sides:
b = sqrt(115mi^2)
Rounding to the nearest tenth:
b ≈ 10.7mi