I am trying to solve the length of the hypotenuse of a right triangle with sides of 6mm and 8mm
For a right angle triangle the following equation is true:
a^2 + b^2 = c^2
Where c is the hypotenuse of the triangle and a,b are the other sides (you decide which side is a and which side is b).
This involves the pythagorean theorem. Let c = hypotenuse; a = 1 side; b = other side.
c^2 = a^2 + b^2
c^2 = 6^2 + 8^2
c^2 = 36 + 64
Solve for c.
I am trying to solve the length of the hypotenuse of a right triangle with sides of 6mm and 8mm
a = 6mm, b = 8mm
For b > a
c = b^2[1 + a^2/b^2]/sqrt(a^2 + b^2)
Regarding:
For b > a
c = b^2[1 + a^2/b^2]/sqrt(a^2 + b^2)
I forgot to acknowledge that when this expression is multipied out, the end result is c = sqrt(a^2 + b^2).
I was initially surprised when deriving it from the relationship between the altitude to the hypotenuse and the hypotenuse itself;
* The altitude to the hypotenuse of a right triangle is the geometric mean between the segments of the hypotenuse created by the point where the altitude intersects the hypotenuse or h^2 = xy.
* With an altitude drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse in contact with the leg.
Can't beat old Pythagorus.
To solve for the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem. 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.
In this case, you have a right triangle with sides of 6mm and 8mm. Let's call the length of the hypotenuse "c".
According to the Pythagorean theorem, we have:
c^2 = 6^2 + 8^2
Simplifying this equation, we get:
c^2 = 36 + 64
c^2 = 100
To find the value of "c", we take the square root of both sides of the equation:
c = √100
c = 10 mm
Therefore, the length of the hypotenuse of the right triangle is 10mm.