In a certain right triangle, the two sides that are perpendicular to each other are 3.80 m and 8.10 m long. What is the length of the third side of the triangle?
c^2 = a^2 + b^2 = 3.8^2 + 8.1^2 =
80.05
To find the length of the third side of the right triangle, we can use the Pythagorean theorem. According to the Pythagorean theorem, in a right triangle, the sum of the squares of the lengths of the two smaller sides is equal to the square of the length of the hypotenuse (the longest side).
In this case, the two sides that are perpendicular to each other, also known as the legs of the triangle, have lengths of 3.80 m and 8.10 m.
Using the Pythagorean theorem, we can set up the equation as follows:
(3.80^2) + (8.10^2) = c^2
Simplifying this equation:
14.44 + 65.61 = c^2
79.05 = c^2
To solve for c, we take the square root of both sides of the equation:
c = √79.05
Using a calculator, we find that √79.05 is approximately equal to 8.89.
Therefore, the length of the third side of the triangle is approximately 8.89 m.