Question

MEDAL!!! The leg of a right triangle is 3 units and the hypotenuse is 11 units. What is the length, in units, of the other leg of the triangle?

Answer 1

For special right triangles, we can apply The Pythagorean Theorem, which states, \((\text{hypotenuse})^2 = (\text{leg 1})^2 + (\text{leg 2})^2\)

Answer 2

by pyth theorem x^2+3^2=11^2

Answer 3

Or it can rather be written as \(c^2 = a^2+b^2\) where c is the hypotneuse, and a and b are the legs.

Now if we are given the length of the hypotenuse and a leg of a triangle, we can rearrange our equation to solve for the leg of the triangle

Answer 4

x^2=121-9

Answer 5

x=sqrt(112)

Answer 6

Therefore, \(11^2 = 3^2 +x^2 \implies x = \sqrt{11^2 -3^2}\)

Answer 7

Now just solve for x and you will find the length of the missing leg :)

Answer 8

so its

Answer 9

yes

Answer 10

ok