Examples
45-45-90 triangle:
An architect is trying to build a triangular roof. he wants the angles of the roof to be 45, 45, and 90 & he knows that he wants the part of the roof that rests on the house (the hypotenuse) to be 20 feet long. He wants to know what the other two side lengths of the roof should be in order for them to form a right triangle. In order to do this, the architect would use the properties of a 45-45-90 triangle. Since he knows the hypotenuse is 20 feet, he would have to divide 20 by the square root of 2. The answer will be the length of the other two sides of the triangular roof.
An architect is trying to build a triangular roof. he wants the angles of the roof to be 45, 45, and 90 & he knows that he wants the part of the roof that rests on the house (the hypotenuse) to be 20 feet long. He wants to know what the other two side lengths of the roof should be in order for them to form a right triangle. In order to do this, the architect would use the properties of a 45-45-90 triangle. Since he knows the hypotenuse is 20 feet, he would have to divide 20 by the square root of 2. The answer will be the length of the other two sides of the triangular roof.
30-60-90 triangle.
An architect is attempting to build a triangular window which he wants to have angles of measures 90, 60, and 30 degrees. He also knows that the longest side of the triangle will be 5 feet long. He wants to find the lengths of the other 2 sides of the window. To do this, he can divide 5 by two 2 get the shortest side length, then multiply that by the square root of 3 to get the medium side length.
An architect is attempting to build a triangular window which he wants to have angles of measures 90, 60, and 30 degrees. He also knows that the longest side of the triangle will be 5 feet long. He wants to find the lengths of the other 2 sides of the window. To do this, he can divide 5 by two 2 get the shortest side length, then multiply that by the square root of 3 to get the medium side length.