The hypotenuse of a right triangle is 35 cm long, and the length of the short sides is 23 cm. Find the length of the other side.
Ah, the hypotenuse and the short sides of a right triangle - they're always up to some shenanigans! Alright, let's figure this out. We can use the good old Pythagorean theorem to solve this one. The theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In equation form, it looks like this:
c^2 = a^2 + b^2
Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. In this case, we know that c is 35 cm, so let's plug in the numbers:
35^2 = 23^2 + b^2
Now, let's do some fancy math - don't worry, I'll do the calculations, just sit back and enjoy the show!
1225 = 529 + b^2
Alright, let's subtract 529 from both sides:
1225 - 529 = b^2
Phew, this is intense. Now, let's simplify it:
696 = b^2
Hmm, getting closer. Now, let's take the square root of both sides:
√696 = √(b^2)
Wait for it...wait for it... It's about to get real!
Approximately, b ≈ 26.4 cm
Tadah! The length of the other side is approximately 26.4 cm. So, when it comes to triangles, it's all about the sides - they're a real sideshow!
To find the length of the other side, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's denote the length of the other side as "x". According to the theorem, we have:
x^2 + 23^2 = 35^2
To solve for x, let's simplify the equation:
x^2 + 529 = 1225
Subtracting 529 from both sides of the equation, we get:
x^2 = 1225 - 529
x^2 = 696
To find the length of the other side, we need to take the square root of both sides of the equation:
x = √696
Using a calculator, we find that the square root of 696 is approximately 26.38.
Therefore, the length of the other side is approximately 26.38 cm.
To find the length of the other side of a right triangle, we can use the Pythagorean theorem. The theorem states that 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 lengths of the other two sides.
Let's denote the length of the other side as 'x'. We have the following information:
Hypotenuse (c) = 35 cm
Short side (a) = 23 cm
Other side (b) = x cm
Using the Pythagorean theorem, we can write the equation:
c^2 = a^2 + b^2
Substituting the given values:
35^2 = 23^2 + x^2
Now we can solve for x by isolating it and simplifying the equation:
1225 = 529 + x^2
Rearranging the equation:
x^2 = 1225 - 529
x^2 = 696
Taking the square root of both sides:
x = √696
x ≈ 26.38 cm
Therefore, the length of the other side (b) is approximately 26.38 cm.
I'm pretty sure you meant math, not physics. Anyways, to solve this problem use the Pythagorean Theorem.
a^2+b^2=c^2
c^2-b^2=a^2
35^2-23^2= a^2
1225-529= 694
The answer is the square root of 694.