This problem involved using the Pythagorean theorem to solve for the missing leg of a right triangle. By substituting the known values and solving the resulting equation, we were able to approximate the length of the missing leg to be Option C) 9.4 inches, rounded to the nearest tenth of an inch.
Let's find the length of the missing leg of a right triangle, given that one leg measures 9 inches and the hypotenuse measures 13 inches. We'll round our answer to the nearest tenth of an inch.
Steps to solve:
Pythagorean Theorem: We can use the Pythagorean theorem to relate the sides of a right triangle. The theorem states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides (the legs). In this case, we can write the equation:
hypotenuse^2 = leg1^2 + leg2^2
Substitute and solve: We are given that the hypotenuse is 13 inches and one leg is 9 inches. Let the missing leg be represented by the variable x. Substituting these values into the equation, we get:
13^2 = 9^2 + x^2
Isolate and solve for x: Solve the equation for x by subtracting 9^2 from both sides and then taking the square root of both sides:
x^2 = 13^2 - 9^2
x = sqrt(169 - 81)
x = sqrt(88)
Approximate the answer: Since the problem asks for the answer rounded to the nearest tenth of an inch, we can approximate the square root of 88 using a calculator or by using the fact that 88 is between 81 (9^2) and 100 (10^2). Therefore, the square root of 88 is approximately between 9 and 10. To get a more precise answer, we can take the square root of 88 and round to the nearest tenth:
x ≈ 2√22 ≈ 9.4 inches (rounded to the nearest tenth)
Answer:
Therefore, the length of the missing leg of the right triangle is approximately 9.4 inches, rounded to the nearest tenth of an inch.
The probable question may be:-
Find the length of a leg of a right triangle whose other leg measures 9 inch and whose hypotenuse is 13 inch . Round your result to the nearest tenth of an inch.
A) 15.8 inches
B) 88 inches
C) 9.4 inches
D) 4 inches