SOLUTION: A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, where c is the hypotenuse (the side opposite the 90

Algebra ->  Triangles -> SOLUTION: A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, where c is the hypotenuse (the side opposite the 90      Log On


   

Question 72631: A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, where c is the hypotenuse (the side opposite the 90° angle). Find the hypotenuse when the other 2 sides’ measurements are 3 feet and 4 feet
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
The Pythagorean theorem says that the sum of the squares of the two legs (short sides) of
a right triangle are equal to the square of the long side (the hypotenuse). In equation
form this is:
.
a%5E2+%2B+b%5E2+=+c%5E2
.
in which "a" and "b" represent the legs and "c" represents the hypotenuse. For this problem
we know that:
.
a+=+3
.
and:
.
b+=+4
.
Substitute these values into the equation for the Pythagorean theorem and you get:
.
3%5E2+%2B+4%5E2+=+c%5E2
.
Now do the calculations. 3%5E2+=+3%2A3+=+9 and 4%5E2+=+4%2A4+=+16. Substitute
these values to get:
.
9+%2B+16+=+c%5E2
.
The addition on the left side gives you:
.
25+=+c%5E2
.
and you now take the square root of both sides to get:
.
c+=+5
.
So the hypotenuse or long side of this right triangle is 5 units long.
.
Just for information, any builder knows about the 3 - 4 - 5 triangle. He or she uses it
to make sure that walls are at right angles. They do this by measuring down one wall 3 feet
and marking that spot. They then measure down the perpendicular wall 4 feet and marking
that spot also. Then they measure the slant distance between the two spots. If that
distance isn't 5 feet exactly, then they know the walls are not really perpendicular to each
other and they will have to adjust the walls until they get the distance between the 3-foot
and 4-foot marks to be exactly 5 feet. Sometimes geometry really is helpful in the real
world.
.
Remember this one. Someday you're going to want to fence something in and you can use
this triangle to make sure the corners of your fence lines are a right angles to each other
(even if you can't remember what the Pythagorean theorem is).
.
Hope this helps you to understand the Pythagorean theorem a little better.