AAS Triangle Calculator

Solving an AAS (Angle-Angle-Side) triangle relies on fundamental geometric principles and trigonometric laws. First, because all interior angles in a Euclidean triangle always sum to 180 degrees, the third angle (gamma) can be calculated immediately using the formula: angle_gamma = 180° - angle_alpha - angle_beta. Once all three angles are known, you can find the remaining two side lengths (sideB and sideC) using the Law of Sines: sideB = sideA * sin(angle_beta) / sin(angle_alpha). Finally, the area and height are derived using standard trigonometric area formulas based on the computed sides and angles.

Let us solve an AAS triangle where angle alpha is 40°, angle beta is 25°, and the known side A is 16 cm. First, find the third angle: gamma = 180° - 40° - 25° = 115°. Next, use the Law of Sines to find side B: sideB = 16 * sin(25°) / sin(40°) = 16 * 0.4226 / 0.6428 = 10.53 cm. Then, find the height using side A and angle gamma: height = 16 * sin(115°) = 16 * 0.9063 = 14.50 cm. Lastly, calculate the total area: area = (16 * 10.53 * sin(115°)) / 2 = 76.31 square centimeters.

Always verify your input angles to ensure their sum is strictly less than 180 degrees before attempting any calculations. When computing trigonometric values manually, remember to check whether your calculator is set to degrees or radians to avoid massive computation errors. Keep intermediate rounding decimals as precise as possible until the final step to ensure maximum accuracy in your final side lengths and area outputs.