Use the Pythagorean theorem to find the unknown side of the right triangle.
7
24
A right triangle has a vertical side of length 7, a horizontal side of length 24, and an unlabeled hypotenuse.
Hypotenuse length
nothing
(Simplify your answer. Type exact answers, using radicals as needed.)
you can save yourself some calculation by memorizing a few of the basic Pythagorean triples, such as
3-4-5, 5-12-13, 7-24-25, 8-15-17
and their multiples
To find the length of the hypotenuse, 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 length of the hypotenuse as c, and the lengths of the other two sides as a and b. In this case, a = 7 and b = 24.
Using the Pythagorean theorem, we have:
c^2 = a^2 + b^2
Plugging in the given values, we get:
c^2 = 7^2 + 24^2
Simplifying this equation:
c^2 = 49 + 576
c^2 = 625
To find the length of the hypotenuse, we take the square root of both sides:
c = √625
The square root of 625 is 25.
Therefore, the length of the hypotenuse is 25 units.
To find the hypotenuse length of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we have a vertical side of length 7 (let's call it A) and a horizontal side of length 24 (let's call it B). Let's use C to represent the hypotenuse length we want to find.
The equation for the Pythagorean theorem is:
A^2 + B^2 = C^2
Substituting the given values:
7^2 + 24^2 = C^2
49 + 576 = C^2
625 = C^2
To find C (the hypotenuse length), we need to take the square root of both sides of the equation:
√625 = √C^2
25 = C
Therefore, the hypotenuse length is 25.