The longer leg of a right triangle is 1 m longer than the shorter leg. the hypotenuse is 9 m longer than the shorter leg find the side lengths of the triangl

Let be the length of the shorter leg.

The other leg is 1m longer, so its length is

The hypothenuse is 9m longer, so its length is

The pythagorean theorem states that the sum of the squares of the legs is the square of the hypothenuse, so we have

Expanding the squares gives

Move all to the left hand side:

This equation has solutions and

We can't accept the first solution, because it would lead to the side lengths

And we can't have negative side lengths.

The other solution is fine, because it leads to the side lengths

So, the side lengths are 20 (shorter leg), 21 (longer leg), 29 (hypothenuse)

  21.3

step-by-step explanation:

multiplying the given equation by c/sin(25°), we get

  c = 9/sin(25°) ≈ 21.2958 ≈ 21.3

we assume "c" is the length of ab, the side opposite angle c in triangle abc.