Find the length of the leg of this right triangle. Give an approximation to 3 decimal places.
hyp=24
adj=22
15cm
7cm
To find the length of the leg of the right triangle, we can use the Pythagorean theorem. The formula for the Pythagorean theorem is a^2 + b^2 = c^2, where a and b are the lengths of the two legs of the right triangle, and c is the length of the hypotenuse.
Given that the hypotenuse (c) is 24 and the adjacent side (a) is 22, we can solve for the length of the other leg (b) using the formula:
b^2 = c^2 - a^2
Substituting the given values:
b^2 = 24^2 - 22^2
Now, we can calculate:
b^2 = 576 - 484
b^2 = 92
Taking the square root of both sides:
b ≈ √92
Using a calculator, the square root of 92 is approximately 9.59.
Therefore, the length of the leg of the right triangle is approximately 9.59 (rounded to 3 decimal places).
To find the length of the leg of a right triangle, we can use the Pythagorean theorem. According to the theorem, 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 other two sides.
In this case, we are given the lengths of the hypotenuse (24) and one of the legs (22). Let's call the length of the missing leg "leg".
So, we have:
hypotenuse^2 = leg^2 + other leg^2
Substituting the given values:
24^2 = leg^2 + 22^2
Simplifying:
576 = leg^2 + 484
Rearranging the equation to solve for the length of the leg:
leg^2 = 576 - 484
leg^2 = 92
Taking the square root of both sides:
leg ≈ √92
Using a calculator, we find that √92 is approximately 9.5917.
Therefore, the length of the leg of the right triangle, rounded to 3 decimal places, is approximately 9.592.
a^2 + b^2 = c^2
a^2 + 22^2 = 24^2
a^2 + 484 = 576
a^2 = 576 - 484
a^2 = 92
A = 9.592