The triangle is the simplest polygon having three tops and three parties. The triangle, one of corners of which is to straight lines, is called rectangular. For rectangular triangles all formulas for triangles of a general view are applicable. However they can be altered, considering properties of a right angle.
Instruction
1. Basic formula for finding of the area of a triangle through and height looks basis as follows: S = 1/2 * b * h where b is the party of a triangle, and h – triangle height. Height of a triangle is the perpendicular which is carried out from triangle top to the straight line containing the opposite side. For a rectangular triangle height to a leg of b coincides with a leg and. Thus, you receive a formula for calculation of the area of a triangle with a right angle: S = 1/2 * a * b.
2. Review an example. Let in a rectangular triangle and = 3, b = 4. Then S = 1/2 * 3 * 4 = 6. Count the area of the same triangle, but now let only one leg of b = 4 is known. And also the corner α is known, to tg α = 3/4. Then from expression for trigonometrical function a tangent of angle α express a leg: tg α = a/b => a = b * tg α. Substitute this value in a formula for calculation of the area of a rectangular triangle and we receive: S = 1/2 * a * b = 1/2 * b^2 * tg α = 1/2 * 16 * 3/4 = 6.
3. Consider calculation of the area of an isosceles rectangular triangle as a special case. The isosceles triangle is a triangle in which two parties are equal among themselves. In case of a rectangular triangle a = b turns out. Write down Pythagorean theorem for this case: c^2 = a^2 + b^2 = 2 * a^2. Further substitute this value in a formula of calculation of the area as follows: S = 1/2 * a * b = 1/2 * a^2 = 1/2 * (c^2/2) = c^2/4.
4. Count the area of an isosceles rectangular triangle. Let the hypotenuse be equal 4 * √2. Then the area of a triangle is calculated as S = by c^2/4 = 16 * 2/4 = 8.
5. If radiuses of the entered r and described R circles are known, then the area of a rectangular triangle is calculated on formula S = by r^2 + 2 * r * R. Let the radius of an inscribed in a triangle circle of r = 1, the radius of R circle described around a triangle = 5/2. Then S = 1 + 2 * 1 * 5/2 = 6.