What Are the Rules for a 45-45-90 Triangle?Ī 45-45-90 triangle has a right angle and two 45 degree angles. The side that is opposite to the 90° angle, 2y will be the largest side because 90° is the largest angle. The side that is opposite to the 60° angle, y√3 will be the medium length because 60° is the mid-sized degree angle in this triangle. The side that is opposite to the 30° angle, 'y' will always be the smallest since 30° is the smallest angle in this triangle. The sides of a 30-60-90 triangle have a set pattern.
What Are the Side Lengths of a 30-60-90 Triangle? A 30-60-90 triangle is a special right triangle that always has angles of measure 30°, 60°, and 90°. The 30-60-90 triangle is called a special right triangle as the angles of this triangle are in a unique ratio of 1:2:3. One can remember it as 1, 3, 2 it can resemble the ratio of the sides, all one needs to remember is that the middle term is √3 What Is a 30-60-90 Triangle? This method can be used to remember the 30-60-90 triangle rule. The perimeter of the triangle is a+a√3+2a = 3a+a√3 = a√3(1+√3) Are There Any Tips for Remembering the 30-60-90 Triangle Rules? The perimeter of a 30 60 90 triangle with the smallest side equal to a is the sum of all three sides. This is called the 30-60-90 triangle rule.įAQs on 30-60-90 Triangle What Is the Perimeter of a 30-60-90 Triangle?
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We have learned in the previous section how to find the hypotenuse when the base is given. Let's learn how to apply this formula to find the area of the 30-60-90 triangle.īase BC of the triangle is assumed to be 'a', and the hypotenuse of the triangle ABC is AC. Thus, the formula to calculate the area of a right-angle triangle is = (1/2) × base × perpendicular In a right-angled triangle, the height is the perpendicular of the triangle. The formula to calculate the area of a triangle is = (1/2) × base × height. The side opposite to the 90° angle, the hypotenuse AC = 2y = 2 × 7 = 14.The side opposite to the 60° angle, BC = y √3 = 7 √3.The side opposite to the 30° angle, AB = y = 7.The side opposite to the 90° angle, the hypotenuse AC = 2y = 2 × 2 = 4.The side opposite to the 60° angle, BC = y √3 = 2 √3.The side opposite to the 30° angle, DE = y = 2.Let us learn the derivation of this ratio in the 30-60-90 triangle proof section.Ĭonsider some of the examples of a 30-60-90 degree triangle with these side lengths: This is also known as the 30-60-90 triangle formula for sides. In a 30-60-90 triangle, the ratio of the sides is always in the ratio of 1:√3: 2. On the side that is opposite to the 90° angle, the hypotenuse AC = 2y will be the largest side because 90° is the largest angle. The side that is opposite to the 60° angle, BC = y × √ 3 = y √ 3 will be the medium length because 60° is the mid-sized degree angle in this triangle The side that is opposite to the 30° angle, AB = y will always be the smallest since 30° is the smallest angle in this triangle
We can understand the relationship between each of the sides from the below definitions: A 30-60-90 triangle is a special triangle since the length of its sides is always in a consistent relationship with one another.