find the length of one leg of a right triangle if the length of the hypotenuse is 18 feet and the length of the other leg is 14 feet. round to the nearest tenth.
14^2 + x^2 = 18^2
x^2 = 18^2 - 14^2 = 324 - 196 = 128 = 2*64 = 2 * 8^2
so
x = 8 sqrt 2 = 11.3137085 or 11.3
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check
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11.3^2 = 128
14^2 = 196
sum = 324
sqrt = 18 , whew !
x^2 + 14^2 = 18^2
x^2 = 324 - 196 =128
x = √128 or 8√2
To find the length of one leg of a right triangle, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
Given that the length of the hypotenuse (c) is 18 feet and the length of the other leg (b) is 14 feet, we can substitute these values into the equation:
a^2 + 14^2 = 18^2
a^2 + 196 = 324
Subtracting 196 from both sides:
a^2 = 324 - 196
a^2 = 128
Now, we can take the square root of both sides to solve for a:
a = √128
a ≈ 11.3
Therefore, the length of one leg of the right triangle is approximately 11.3 feet (rounded to the nearest tenth).
To find the length of one leg of a right triangle, you can use the Pythagorean theorem, which 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 lengths of the other two legs.
Let's denote the length of the unknown leg as x.
Using the Pythagorean theorem, we have:
x^2 + 14^2 = 18^2
Simplifying this equation:
x^2 + 196 = 324
Subtracting 196 from both sides:
x^2 = 324 - 196
x^2 = 128
Now, take the square root of both sides to solve for x:
x = √128 = 11.31 (approximately)
Therefore, the length of one leg of the right triangle is approximately 11.31 feet when rounded to the nearest tenth.