write 30° -60° -90° property. and 45° -45° -90° property
Answers
1) Qualities of a 30-60-90 Triangle
Qualities of a 30-60-90 TriangleA 30-60-90 triangle is special because of the relationship of its sides. Hopefully, you remember that the hypotenuse in a right triangle is the longest side, which is also directly across from the 90 degree angle. It turns out that in a 30-60-90 triangle, you can find the measure of any of the three sides, simply by knowing the measure of at least one side in the triangle.
Qualities of a 30-60-90 TriangleA 30-60-90 triangle is special because of the relationship of its sides. Hopefully, you remember that the hypotenuse in a right triangle is the longest side, which is also directly across from the 90 degree angle. It turns out that in a 30-60-90 triangle, you can find the measure of any of the three sides, simply by knowing the measure of at least one side in the triangle.The hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle. The longer leg, which is across from the 60 degree angle, is equal to multiplying the shorter leg by the square root of 3. This picture shows this relationship with x representing the shorter leg.
Of course, to go in the opposite direction you can divide, instead of multiply, by the appropriate factor. Thus, the relationships can be summarized like this:
Of course, to go in the opposite direction you can divide, instead of multiply, by the appropriate factor. Thus, the relationships can be summarized like this:Shorter leg ---> Longer Leg: Multiply by square root of 3
Of course, to go in the opposite direction you can divide, instead of multiply, by the appropriate factor. Thus, the relationships can be summarized like this:Shorter leg ---> Longer Leg: Multiply by square root of 3Longer leg ---> Shorter Leg: Divide by square root of 3
Of course, to go in the opposite direction you can divide, instead of multiply, by the appropriate factor. Thus, the relationships can be summarized like this:Shorter leg ---> Longer Leg: Multiply by square root of 3Longer leg ---> Shorter Leg: Divide by square root of 3Shorter Leg ---> Hypotenuse: Multiply by 2
Of course, to go in the opposite direction you can divide, instead of multiply, by the appropriate factor. Thus, the relationships can be summarized like this:Shorter leg ---> Longer Leg: Multiply by square root of 3Longer leg ---> Shorter Leg: Divide by square root of 3Shorter Leg ---> Hypotenuse: Multiply by 2Hypotenuse ---> Shorter Leg: Divide by 2
2) When we are talking about a 45-45-90 triangle, those numbers represent the measures of the angles of that triangle. So, it means the triangle has two 45-degree angles and one 90-degree angle.
When we are talking about a 45-45-90 triangle, those numbers represent the measures of the angles of that triangle. So, it means the triangle has two 45-degree angles and one 90-degree angle.Let's do a little origami to make one of these triangles! Don't worry; you don't have to make a swan! Origami is usually made using a square piece of paper. Imagine you take a square and fold it so that two of the corners end up on top of each other, like this:
We placed corner B on corner D and made a crease diagonally through corners A and C. Now we have made a triangle. Since we did not cut anything off the paper, we know several things about that triangle. The angle at D is a right angle (measures 90 degrees) because the square had four right angles. The angles A and C must each be 45 degrees because the right angles there were folded exactly in half. Since we folded exactly through the corners, the lengths of the sides AD and DC did not change from what they were in the square. Therefore, we know that the sides AD and DC must be of equal length because on the square, all of the sides were of equal length.
We placed corner B on corner D and made a crease diagonally through corners A and C. Now we have made a triangle. Since we did not cut anything off the paper, we know several things about that triangle. The angle at D is a right angle (measures 90 degrees) because the square had four right angles. The angles A and C must each be 45 degrees because the right angles there were folded exactly in half. Since we folded exactly through the corners, the lengths of the sides AD and DC did not change from what they were in the square. Therefore, we know that the sides AD and DC must be of equal length because on the square, all of the sides were of equal length.Doing this little folding exercise, we have discovered that every 45-45-90 triangle has two sides with the same length. Those sides are called the legs of the triangle. The hypotenuse (the side opposite of the right angle) will always have a length longer than the legs. In the next two sections, we will talk about the formula to calculate the length of the hypotenuse and the theorem for 45-45-90 triangles.
Hope it will help you..