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If the measure of the non-hypotenuse sides is x, then the measure of the hypotenuse is √2 * x. What is a Special Right Triangle Special right triangles are triangles whose sides are in a particular ratio, known as Pythagorean Triples. The other special right triangle you should be familiar with before taking the ACT or SAT is the other one in the figure above: the 45-45-90 triangle. How simple was that? Pretty darn, if you ask us! By taking one look at the figure and doing one simple calculation, we solved the problem and shaved off precious time from our total test. So, in our original problem, the shortest side is 4, so we know that the hypotenuse is two times that: 8. If the shortest side-the side opposite the 30-degree angle-is x, then the measure of the other side is √3 * x, and the hypotenuse measures 2 x. In a 30-60-90 triangle, the sides follow the pattern in the figure above.
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This triangle, with angles of 30, 60, and 90 degrees, is a special kind of right triangle with specific properties you should be familiar with. Special Right Triangles Puzzle This cut-out puzzle was created to help students find missing sides in special right triangles, including both 45°-45°-90° and 30°-60°-90° triangles.
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However, there is another way we can approach this problem, one that can save us A LOT of time! 8, 37, 12 3 5.2 Special Right Triangles Investigating. Although all right triangles have special features trigonometric functions and the Pythagorean theorem.The most frequently studied right triangles, the special right triangles, are the 30, 60, 90 Triangles followed by the 45, 45, 90 triangles. since sin = opposite/hypotenuse, we know that c must be 8, and 4/8 = 0.5. Pythagorean Triple: Example 2: Leave you answers as a simplified radical. A 45°-45°-90° triangle is one type of special. So another name for an isosceles right triangle is a 45°-45°-90° triangle. Since the base angles of an isosceles triangle are congruent, the measure of each acute angle is 45°. Using our graphing calculator and SOH-CAH-TOA, we can enter sin(30) (making sure we’re in degree mode!), giving us a value of 0.5. 5-8 Applying Special Right Triangles A diagonal of a square divides it into two congruent isosceles right triangles. Our next hope could be to use our trigonometric functions. However, with the measure of only one side, we can’t use this method to find c. Seeing a right triangle, your first instinct might be to try the Pythagorean theorem. A special right-triangle is a right triangle whose sides are. In the figure to the left, what is the measure of c? Recognizing special right triangles in geometry can help you to answer some questions quicker.