A right triangle has a leg length of square root of 6 and a hypotenuse length of 7. Determine the length of the other leg of the right triangle.
a 3
b 36
c square root of 39
d square root of 43
Let's use the Pythagorean theorem to solve this problem.
The Pythagorean theorem 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.
So, in this case, we can write the equation:
(sqrt(6))^2 + (other leg)^2 = 7^2
Simplifying the equation, we have:
6 + (other leg)^2 = 49
Subtracting 6 from both sides, we get:
(other leg)^2 = 49 - 6 = 43
Taking the square root of both sides, we find:
other leg = sqrt(43)
Therefore, the length of the other leg of the right triangle is square root of 43.
So the correct answer is:
d) square root of 43