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If a right triangle has a leg that is 6 ft. long and the hypotenuse is 12 ft. long, how long is the other leg? Round to the nearest tenth.
If a right triangle has a leg that is 6 ft. long and the hypotenuse is 12 ft. long, how long is the other leg? Round to the nearest tenth.
Answers
Answered by
GPT 3.5
To find the length of the other leg of the right triangle, you 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).
In this case, we are given that one leg (a) is 6 ft and the hypotenuse (c) is 12 ft. Let's denote the other leg as b.
According to the Pythagorean theorem, we can write the equation:
a^2 + b^2 = c^2
Substituting the given values:
6^2 + b^2 = 12^2
36 + b^2 = 144
Now, subtract 36 from both sides of the equation:
b^2 = 144 - 36
b^2 = 108
Finally, take the square root of both sides to find the value of b:
b ≈ √108
b ≈ 10.3923
Rounding to the nearest tenth, the length of the other leg of the right triangle is approximately 10.4 ft.
In this case, we are given that one leg (a) is 6 ft and the hypotenuse (c) is 12 ft. Let's denote the other leg as b.
According to the Pythagorean theorem, we can write the equation:
a^2 + b^2 = c^2
Substituting the given values:
6^2 + b^2 = 12^2
36 + b^2 = 144
Now, subtract 36 from both sides of the equation:
b^2 = 144 - 36
b^2 = 108
Finally, take the square root of both sides to find the value of b:
b ≈ √108
b ≈ 10.3923
Rounding to the nearest tenth, the length of the other leg of the right triangle is approximately 10.4 ft.
Answered by
GPT 3.5
Apologies for the confusion. In a right triangle, the lengths of the sides are typically denoted as a, b, and c, with a and b representing the legs and c representing the hypotenuse.
Given that one leg (a) is 6 ft and the hypotenuse (c) is 12 ft, you are trying to find the length of the other leg (b).
To find the length of b, you can use the Pythagorean theorem, which states that a^2 + b^2 = c^2.
Let's solve for b:
a = 6 ft
c = 12 ft
Using the Pythagorean theorem:
6^2 + b^2 = 12^2
36 + b^2 = 144
To solve for b^2, subtract 36 from both sides:
b^2 = 144 - 36
b^2 = 108
Finally, take the square root of both sides to find the value of b:
b ≈ √108
b ≈ 10.3923
Rounding to the nearest tenth, the length of the other leg (b) is approximately 10.4 ft.
Given that one leg (a) is 6 ft and the hypotenuse (c) is 12 ft, you are trying to find the length of the other leg (b).
To find the length of b, you can use the Pythagorean theorem, which states that a^2 + b^2 = c^2.
Let's solve for b:
a = 6 ft
c = 12 ft
Using the Pythagorean theorem:
6^2 + b^2 = 12^2
36 + b^2 = 144
To solve for b^2, subtract 36 from both sides:
b^2 = 144 - 36
b^2 = 108
Finally, take the square root of both sides to find the value of b:
b ≈ √108
b ≈ 10.3923
Rounding to the nearest tenth, the length of the other leg (b) is approximately 10.4 ft.
Answered by
GPT 3.5
Based on the given information, we have a right triangle with the hypotenuse (c) measuring 30 units and one leg (b) measuring 20 units. We need to find the length of the other leg (a).
Using the Pythagorean theorem, which states that a^2 + b^2 = c^2, we can substitute the given values into the equation:
a^2 + 20^2 = 30^2
Simplifying:
a^2 + 400 = 900
Now, subtract 400 from both sides of the equation:
a^2 = 500
To find the value of a, take the square root of both sides:
a ≈ √500
a ≈ 22.36
Rounded to the nearest hundredth, the length of the other leg of the right triangle is approximately 22.36 units.
Using the Pythagorean theorem, which states that a^2 + b^2 = c^2, we can substitute the given values into the equation:
a^2 + 20^2 = 30^2
Simplifying:
a^2 + 400 = 900
Now, subtract 400 from both sides of the equation:
a^2 = 500
To find the value of a, take the square root of both sides:
a ≈ √500
a ≈ 22.36
Rounded to the nearest hundredth, the length of the other leg of the right triangle is approximately 22.36 units.