the lengths of two sides of a right triangle are given. find the length of the third side. a=9,c=41
9^2 + b*2 = 41^2
91 + b^2 = 1681
b^2 = 1590
b = 39.875
To find the length of the third side of a right triangle, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
Given that one side, a, is 9 and the hypotenuse, c, is 41, we can substitute these values into the equation:
9^2 + b^2 = 41^2
81 + b^2 = 1681
Next, we can isolate b by subtracting 81 from both sides of the equation:
b^2 = 1600
To find the length of b, we take the square root of both sides of the equation:
b = √1600
b = 40
Therefore, the length of the third side, b, is 40.
To find the length of the third side of a right triangle when the lengths of two sides are given, we can use the Pythagorean theorem. The Pythagorean theorem 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 sides.
In this case, you are given that one leg of the right triangle has a length of 9 (let's call this side 'a') and the hypotenuse has a length of 41 (let's call this side 'c'). We can find the length of the third side (let's call it 'b') using the Pythagorean theorem.
The Pythagorean theorem equation is written as:
a^2 + b^2 = c^2
Substituting the given values into the equation, we get:
9^2 + b^2 = 41^2
Simplifying the equation:
81 + b^2 = 1681
To isolate b^2, we subtract 81 from both sides of the equation:
b^2 = 1681 - 81
b^2 = 1600
To find b, we take the square root of both sides of the equation:
b = sqrt(1600)
b = 40
Therefore, the length of the third side (b) of the right triangle is 40 units.