the hypotenuse of a right triangle is 15 units long. if one of the legs is 12 units long, how long is the other leg
We can use the Pythagorean theorem to solve this.
The Pythagorean theorem 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 sides (a and b).
So, in this case, we have:
c^2 = a^2 + b^2
Given that one leg (a) is 12 units long and the hypotenuse (c) is 15 units long, we can substitute these values into the equation:
15^2 = 12^2 + b^2
Simplifying this equation:
225 = 144 + b^2
Subtracting 144 from both sides:
81 = b^2
Taking the square root of both sides, we get:
b = 9
Therefore, the other leg of the right triangle is 9 units long.
two sides of a right triangle measure 5 in and 12 in. if the third side is longer than the either of these sides, what is its measure
Let's assume that the longer side of the right triangle is represented by "x".
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
So, in this case, we have:
x^2 = 5^2 + 12^2
x^2 = 25 + 144
x^2 = 169
To find the value of "x", we need to take the square root of both sides of the equation:
x = √169
x = 13
Therefore, if the third side of the right triangle is longer than either of the other two sides, its measure is 13 inches.
if the hypotenuse is 41 inches, and one of the legs is 9 inches what is the other length of the other leg
We can use the Pythagorean theorem to solve for the length of the other leg.
The Pythagorean theorem 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 sides (a and b).
So, in this case, we have:
c^2 = a^2 + b^2
Given that the hypotenuse (c) is 41 inches and one leg (a) is 9 inches, we can substitute these values into the equation:
41^2 = 9^2 + b^2
Simplifying this equation:
1681 = 81 + b^2
Subtracting 81 from both sides:
1600 = b^2
Taking the square root of both sides, we get:
b = √1600
b = 40
Therefore, the length of the other leg of the right triangle is 40 inches.