If the length of the shorter leg of a right triangle is 5cm and the length of the hypotenuse is 8cm what is the length of the longer leg ?

Question

I don't really know how to do this I need an explanation to help understand so help please its my math I believe its algebra but I'm kindve struggling as you can see but whoever helps please leave an explanation on how you got the answer .

Answer 1

The lengths of the 3 sides of a right triangle are related by the Pythagorean Theorem. That theorem states that the square of the hypotenuse length is equal to the sum of the squares of the other two sides.

Let us say that the length of the hypotenuse is c, the length of one of the other sides is a, and the length of the third side is b.

Then according to this theorem:

a^2 + b^2 = c^2

 

For this problem, c = 8, and a = 5

(Note: You could set b = 5 and make a the variable, it does not matter since you will come up with the same answer)

 

After plugging in the numbers to the equation above:

 25 + b^2 = 64

b^2 = 64-25 = 39

b = sqrt (39) = 6.245

 

So the length of the longer leg is 6.245