Exercise 15 Page 644

We are told that a 45^(∘)-45^(∘)-90^(∘) triangle has a hypotenuse length of 11 and we want to find the length of its leg. To do so, we will start by drawing a diagram to illustrate the situation. Let x be the length of the leg of the triangle.

In a 45^(∘)-45^(∘)-90^(∘) triangle, the legs are congruent and the hypotenuse is sqrt(2) times the length of a leg. With this information, we can find the value of x.

We have that the length of the leg of our triangle is 11sqrt(2)2.