One of the legs of a right triangle measures 6 cm and its hypotenuse measures 9 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Using the Pythagorean Theorem, we can solve for the missing leg, which we'll call "x":
a^2 + b^2 = c^2
(6)^2 + x^2 = (9)^2
36 + x^2 = 81
x^2 = 81 - 36
x^2 = 45
x = √45
x ≈ 6.7 cm (rounded to the nearest tenth)
Therefore, the measure of the other leg is approximately 6.7 cm.
To find the measure of the other leg of the 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 lengths of the other two sides.
Let's denote the other leg as x. We know that one leg measures 6 cm and the hypotenuse measures 9 cm.
Using the Pythagorean theorem, we can set up the following equation:
x^2 + 6^2 = 9^2
Simplifying, we have:
x^2 + 36 = 81
Next, we subtract 36 from both sides:
x^2 = 45
To find the value of x, we take the square root of both sides:
x = √45
Using a calculator, we can find that the square root of 45 is approximately 6.71.
Therefore, the measure of the other leg is approximately 6.71 cm.