Triangle Figure Angle-Side-Angle (ASA)A = angle A B = angle B C = angle C a = side a b = side b c = side c Show
P = perimeter Calculator UseEach calculation option, shown below, has sub-bullets that list the sequence of methods used in this calculator to solve for unknown angle and side values including Sum of Angles in a Triangle, Law of Sines and Law of Cosines. These are NOT the ONLY sequences you could use to solve these types of problems.
Solving Triangle TheoremsAAA is Angle, Angle, AngleSpecifying the three angles of a triangle does not uniquely identify one triangle. Therefore, specifying two angles of a tringle allows you to calculate the third angle only. Given the sizes of 2 angles of a triangle you can calculate the size of the third angle. The total will equal 180° or π radians. C = 180° - A - B (in degrees) C = π - A - B (in radians) AAS is Angle, Angle, SideGiven the size of 2 angles and 1 side opposite one of the given angles, you can calculate the sizes of the remaining 1 angle and 2 sides. use the Sum of Angles Rule to find the other angle, then use The Law of Sines to solve for each of the other two sides. ASA is Angle, Side, AngleGiven the size of 2 angles and the size of the side that is in between those 2 angles you can calculate the sizes of the remaining 1 angle and 2 sides. use the Sum of Angles Rule to find the other angle, then use The Law of Sines to solve for each of the other two sides. ASS (or SSA) is Angle, Side, SideGiven the size of 2 sides (a and c where a < c) and the size of the angle A that is not in between those 2 sides you might be able to calculate the sizes of the remaining 1 side and 2 angles, depending on the following conditions. For A ≥ 90° (A ≥ π/2): If a ≤ c there there are no possible triangles Example: If a > c there is 1 possible solution
For A < 90° (A < π/2): If a ≥ c there is 1 possible solution
If a < c we have 3 potential situations. "If sin(A) < a/c, there are two possible triangles satisfying the given conditions. If sin(A) = a/c, there is one possible triangle. If sin(A) > a/c, there are no possible triangles." [1] sin(A) < a/c, there are two possible triangles solve for the 2 possible values of the 3rd side b = c*cos(A) ± √[ a2 - c2 sin2 (A) ][1] for each set of solutions, use The Law of Cosines to solve for each of the other two angles present 2 full solutions Example: sin(A) = a/c, there is one possible triangle use The Law of Sines to solve for an angle, C use the Sum of Angles Rule to find the other angle, B use The Law of Sines to solve for the last side, b Example: sin(A) > a/c, there are no possible triangles Error Notice: sin(A) > a/c so there are no solutions and no triangle! Example: SAS is Side, Angle, SideGiven the size of 2 sides (c and a) and the size of the angle B that is in between those 2 sides you can calculate the sizes of the remaining 1 side and 2 angles. use The Law of Cosines to solve for the remaining side, b determine which side, a or c, is smallest and use the Law of Sines to solve for the size of the opposite angle, A or C respectively.[2] use the Sum of Angles Rule to find the last angle SSS is Side, Side, SideGiven the sizes of the 3 sides you can calculate the sizes of all 3 angles in the triangle. use The Law of Cosines to solve for the angles. You could also use the Sum of Angles Rule to find the final angle once you know 2 of them. Sum of Angles in a TriangleIn Degrees A + B + C = 180° In Radians A + B + C = π Law of SinesIf a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of sines states: a/sin A = b/sin B = c/sin C Solving, for example, for an angle, A = sin-1 [ a*sin(B) / b ] Law of CosinesIf a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of cosines states: a2 = c2 + b2 - 2bc cos A, solving for cos A, cos A = ( b2 + c2 - a2 ) / 2bc b2 = a2 + c2 - 2ca cos B, solving for cos B, cos B = ( c2 + a2 - b2 ) / 2ca c2 = b2 + a2 - 2ab cos C, solving for cos C, cos C = ( a2 + b2 - c2 ) / 2ab Solving, for example, for an angle, A = cos-1 [ ( b2 + c2 - a2 ) / 2bc ] Other Triangle CharacteristicsTriangle perimeter, P = a + b + c Triangle semi-perimeter, s = 0.5 * (a + b + c) Triangle area, K = √[ s*(s-a)*(s-b)*(s-c)] Radius of inscribed circle in the triangle, r = √[ (s-a)*(s-b)*(s-c) / s ] Radius of circumscribed circle around triangle, R = (abc) / (4K) References/ Further Reading[1] Weisstein, Eric W. "ASS Theorem." From MathWorld-- A Wolfram Web Resource. ASS Theorem. [2] Math is Fun - Solving SAS Triangles Zwillinger, Daniel (Editor-in-Chief). CRC Standard Mathematical Tables and Formulae, 31st Edition New York, NY: CRC Press, p. 512, 2003. Weisstein, Eric W. "Triangle Properties." From MathWorld-- A Wolfram Web Resource. Triangle Properties. Math is Fun at Solving Triangles. How do you find the perimeter of a triangle with 3 points calculator?How do you calculate the perimeter of triangle using points?. Calculate the length of the side AB using the distance formula AB = √(x₂ − x₁)² + (y₂ − y₁)² .. Similarly, find the lengths of the sides BC and AC using the distance formula.. Add the lengths of the three sides to obtain the triangle ABC 's perimeter.. What is the area of the triangle calculator?Triangle area formula
area = 0.5 * b * h , where b is the length of the base of the triangle, and h is the height/altitude of the triangle.
How do you find a triangles perimeter?Perimeter of a triangle = sum of all three sides
Also, the unit of a triangle's perimeter is the same as the units of the lengths of its sides. In case, the units of lengths of its sides are different, then first convert them into the same unit. Example 1: Find the perimeter of the given triangle.
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