Special Right triangles

Today the lesson was on special right triangles.

Today’s Objective: Students will be able to label each side of the special right triangle given the angle measurements and one side length.

Today’s TEKS: G.5(D) identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90).

There are two types of special right triangles that we learned about.

45-45-90 Triangle – Given an isosceles right triangle, the two legs are equal to each other (say x) and the hypotenuse is equal to the square root of 2 multiplied by the leg length (x√2).

30-60-90 Triangle – Given a right triangle with angle measures 30°, 60°, and 90° the leg across from the 30° angle has the shortest side length (say x), the leg across from the 60° angle has a side length equal to the square root of three multiplied by the shortest leg length (x√3), and the hypotenuse is double the length of the shortest leg length (2x).

Question:  If I have a 45-45-90 triangle and I am given the hypotenuse has length 3, how can I find the length of each leg?