the shorter leg of a right triangle is 5 yards.if the hypotenuse is 13 yards,how long is the other leg?
Use the following:
a^2 + b^2 = c^2
a^2 + 5^2 = 13^2
a^2 + 25 = 169
Subtract 25 from both sides (whatever operation you do to one side of an equation you must do to the other side as well):
a^2 = 144
Take the square root of both sides:
a = 12
Hope this helps.
thank you!!
To find the length of the other leg of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's denote the length of the shorter leg as 'a', the length of the other leg as 'b', and the length of the hypotenuse as 'c'.
According to the given information:
a = 5 yards
c = 13 yards
Using the Pythagorean theorem, we can write the equation as:
a^2 + b^2 = c^2
Substituting the given values, we have:
5^2 + b^2 = 13^2
25 + b^2 = 169
Now, let's solve for b by isolating it:
b^2 = 169 - 25
b^2 = 144
To find the value of b, we need to take the square root of both sides of the equation:
sqrt(b^2) = sqrt(144)
b = 12
Therefore, the length of the other leg of the right triangle is 12 yards.
To find the length of the other leg of a right triangle, we can utilize the Pythagorean theorem. This theorem states that in any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we are given that one leg of the right triangle is 5 yards and the hypotenuse is 13 yards. Let's call the other leg "x."
Therefore, using the Pythagorean theorem:
x^2 + 5^2 = 13^2
Simplifying the equation:
x^2 + 25 = 169
Now, we can isolate x by subtracting 25 from both sides of the equation:
x^2 = 169 - 25
x^2 = 144
To find the value of x, we take the square root of both sides:
√x^2 = √144
x = ±12
Since we are considering lengths, the negative value is not meaningful; therefore, the other leg of the right triangle is 12 yards.