In a right triangle the length of a hypotenuse is c and the length of one leg is a. Find the length of the other leg b, if:
c=5, a=3;
a^2 + b^2 = c^2.
3^2 + b^2 = 5^2.
9 + b^2 = 25,
b^2 = 25-9,
Well, since we're talking about right triangles, I guess it's fair to say that getting the length of the other leg is a "legitimate" concern.
Now, let's use a little math clownery to solve this. We can use the Pythagorean Theorem to find the length of the other leg. According to it, the sum of the squares of the lengths of the two legs in a right triangle is equal to the square of the length of the hypotenuse. So we have:
a^2 + b^2 = c^2
Plugging in the values, we get:
3^2 + b^2 = 5^2
Simplifying, we have:
9 + b^2 = 25
Moving things around a little, we find:
b^2 = 16
Taking the square root of both sides, we get:
b = 4
So, the length of the other leg, b, is 4. There you have it - the "leg-endary" answer!
To find the length of the other leg, b, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two legs (a and b).
Using this theorem, we can calculate b as follows:
c^2 = a^2 + b^2
Replacing the given values, we have:
5^2 = 3^2 + b^2
Simplifying:
25 = 9 + b^2
Subtracting 9 from both sides:
16 = b^2
To find the value of b, we take the square root of both sides:
√16 = √b^2
This gives us:
4 = b
Therefore, in the given right triangle, when c = 5 and a = 3, the length of the other leg, b, is 4.
To find the length of the other leg, b, of a right triangle when the length of the hypotenuse (c) and one leg (a) are given, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
So, we can use the formula:
c^2 = a^2 + b^2
In this case, c is given as 5 and a is given as 3. Plugging in these values into the formula, we have:
5^2 = 3^2 + b^2
Simplifying:
25 = 9 + b^2
Now, we can solve for b^2:
b^2 = 25 - 9
b^2 = 16
To find b, we take the square root of both sides:
b = √16
b = 4
Therefore, the length of the other leg, b, is 4.