In a right triangle, a and b represent legs and c represents the hypotenuse. Determine the measure of side b if a = 25.5 m and c = 32.5 m. Express the answer to the nearest tenth meter.
To determine the measure of side b, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
Using the Pythagorean theorem, we can write the equation as:
b^2 = c^2 - a^2
Substituting the given values of a = 25.5 m and c = 32.5 m into the equation, we get:
b^2 = (32.5 m)^2 - (25.5 m)^2
b^2 = 1056.25 m^2 - 650.25 m^2
b^2 = 406 m^2
Taking the square root of both sides to solve for b, we have:
b ≈ √406 ≈ 20.1 m
Therefore, the measure of side b is approximately 20.1 meters (to the nearest tenth meter).