In a right triangle the length of a hypotenuse is c and the length of one leg is a. Find the length of the other leg b, if:
c=13, a=5;
a^2 + b^2 = c^2 or at least used to be
so
25 + b^2 = 169
b^2 = 144
b = 12
which of course you knew anyway because like 3,4,5 the 5,12,13 triangle is a famous right triangle that everyone knows by heart.
To find the length of the other leg b, we 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 sides (a and b).
The Pythagorean theorem is expressed mathematically as:
c^2 = a^2 + b^2
Given:
c = 13
a = 5
We can substitute these values into the equation:
13^2 = 5^2 + b^2
Simplifying, we have:
169 = 25 + b^2
Subtracting 25 from both sides:
b^2 = 169 - 25
b^2 = 144
To solve for b, we take the square root of both sides:
b = √144
Simplifying further:
b = 12
So, the length of the other leg b is 12.
To find the length of the other leg, b, 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 lengths of the other two sides.
The Pythagorean Theorem equation is:
a^2 + b^2 = c^2
Given that c = 13 and a = 5, we can substitute these values into the equation and solve for b:
5^2 + b^2 = 13^2
25 + b^2 = 169
b^2 = 169 - 25
b^2 = 144
To find b, we need to take the square root of both sides of the equation:
√(b^2) = √144
b = 12
Therefore, the length of the other leg, b, is 12.