21/7 = 3 and 28/7 = 4, so this must be a 3-4-5 triangle. Which of the following could be the lengths of the sides of a 45°-45°-90° triangle Find the value of y. First, reduce the side lengths by a common denominator. Let’s figure out which side-based special right triangle this is. 13♴ = 52, so the 3rd side length is 52.Ī triangle has side lengths of 21 and 28. So, the 3rd side length is 2♵ = 10.Ī triangle has side lengths of 20 and 48. We can see from the two given sides that a = 5 and we are missing the 2a side. The 30-60-90 relationship tells us that the side lengths are a, 2a, and a√3. This must be a 30-60-90 triangle because of the two given angles. Ī triangle has side two internal angles of 30° and 90°, and two side lengths of 5 and. Since the leg is 10, the hypotenuse/ 3rd side length is. The 45-45-90 triangle relationship tells us that the hypotenuse is square root of 2 times the leg. How high is the main stage if the ramp has an incline of 45 degrees?Ģ. Find the unknown lengths of the sides in the triangles below:ī.A 45-45-90 triangle has two sides with a length of 10. How high is the main stage if the ramp has an incline of 60 degrees?Ĭ. If the ramp is 20 meters long and has an incline of 30 degrees, how high is the main stage?ī. A rock band uses a ramp at a theater to load and unload the equipment from the main stage. So, we can use that theorem to solve for s.Ī. We can use the 30 o-60 o-90 o Triangle Theorem.įind the length of s in the following triangle:īecause this shape is a right triangle, and the two sides have the same length, s, it must be a 45 o- 45 o- 90 o triangle. In a triangle with the angles 45 o, 45 o, and 90 o, the hypotenuse is times as long as each leg.įind the length of side L and hypotenuse H:īecause the triangle has 30-, 60-, and 90-degree angles, In a triangle that has the angles 30, 60, and 90 degrees, the hypotenuse is 2 times as long as the shorter leg, and the longer leg is times as long as the shorter leg. Right triangles with angles that measure 45 o- 45 o- 90 o or 30 o- 60 o- 90 o are called special right triangles. All right triangles have special properties, but there are certain ones that have some features that make it easier to calculate the length of a missing. Why don’t you use the Pythagorean Theorem to test these relationships? Ask your tutor if you need a hand with this. Length of side a : length of side b: length of side c = 3: 4: 5Īnother one of these relationships is the 5-12-13 triangles. There are several examples of right triangles, but there are two common ratios for side a: side b: side c. One example is the 3-4-5 triangle: Where c is the length of the hypotenuse. Let us write the equation now and then solve for x.ĭoes it make sense? Since the sides of the triangle represent a length, an answer of -11.1249 does not seem reasonable. Where b is the length of the longest leg. Let x be the length of the shortest leg, so if we use the a, b, and c notation we have If the hypotenuse will be 15 yards longer than the longest side, what are the sides of the triangle? For example, if a window built on a building is meant to be a special 30-60-90 triangle, and one side is given, to find the lengths of the other sides, you can use the properties of special right triangles. Th ey decide that the longest side will be 30 yards longer than 3 times the length of the shortest side. Special right triangles can be used in to more easily find the length of a missing side for a triangle. A government agency decides to build a memorial park in the shape of a right triangle.