The hypotenuse is the longest side, opposite the right angle. In a right triangle with sides A, B, and hypotenuse C, the theorem states that A² + B² C². Let's start with the trigonometric triangle area formula:Īrea = (1/2) × a × b × sin(γ), where γ is the angle between the sides. The Pythagorean theorem is a cornerstone of math that helps us find the missing side length of a right triangle. A scalene right triangle is one where all the angles are unequal, and all the sides are unequal in length. An isosceles right triangle is a special isosceles triangle that has two angles that are 45 degrees and legs a and b of equal length. For example, in the triangle at right, sin 4 7, because ABC is a right triangle. Substituting h into the first area formula, we obtain the equation for the equilateral triangle area: Right triangles can be broken into two categories: isosceles and scalene. We must use the sides of a right triangle to calculate the sine of an angle. One leg of that right triangle is equal to height, another leg is half of the side, and the hypotenuse is the equilateral triangle side.Īfter simple transformations, we get a formula for the height of the equilateral triangle: The most important rule is that this triangle has one right angle, and two other angles are equal to 45°. See our right triangle calculator to learn more about right triangles. Height of the equilateral triangle is derived by splitting the equilateral triangle into two right triangles. The basic formula for triangle area is side a (base) times the height h, divided by 2: H = a × √3 / 2, where a is a side of the triangle.īut do you know where the formulas come from? You can find them in at least two ways: deriving from the Pythagorean theorem (discussed in our Pythagorean theorem calculator) or using trigonometry. The formula for a regular triangle area is equal to the squared side times the square root of 3 divided by 4:Īnd the equation for the height of an equilateral triangle looks as follows:
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