Mobile network operators can establish your location by triangulating your signal using 3 or more base towers which are in range. More advanced applications are crucial to surveying and GPS (triangulation). Steel and wooden structures like houses, bridges, warehouses, etc. If you want to know how long a ladder should be so it can reach a given height at a given angle with the ground. The reference lines are established using the 3-4-5 rule. Practical application of triangle geometryĪn everyday use of triangle math is if you want to lay tiles at perfect 90° or 45° to the sides of a room. Obviously using both a tangent calculator and an exponent calculator is quite helpful. This task can be resolved using the ASA rule. So (6 x 4) / 2 = 24 / 2 = 12 sq in.Įxample 3: Find the area of a triangle-shaped garden given one side of it (say, c) is 15 feet long and the two adjacent angles are 30° and 60°. In this case the SAS rule applies and the area can be calculated by solving (b x c x sinα) / 2 = (10 x 14 x sin(45)) / 2 = (140 x 0.707107) / 2 = 99 / 2 = 49.5 cm 2.Įxample 2: If one side of the triangle is known to be 6 inches in length, and the height perpendicular to it is 4 inches in length, what is the triangle's area? This is a straightforward application of the side and height rule which calls for a simple multiplication of the two, and then a division by two. Examples: find the area of a triangleĮxample 1: Using the illustration above, take as given that b = 10 cm, c = 14 cm and α = 45°, and find the area of the triangle. cosγ using the side and angle notations from our calculator graph above.Īnother rule, supported by our calculator is just for right-angled triangles: if you are given the length of the hypotenuse and one of the other sides, you can easily compute the third side using the Pythagorean theorem, and then use it again to get to one of the heights.The law of sines basically states that each side and its opposing angle's sine are related in the same way: The law of cosines is a generalization of the Pythagorean theorem and it tells us that c 2 = a 2 + b 2 - 2ab Some of the above rules rely on the Law of Sines and the Law of Cosines, making it a requirement for you to understand them before you can apply these rules without the help of our area of a triangle calculator. ASA (angle-side-angle) - having the measurements of two angles and the side which serves as an arm for both (is between them), you can fully solve the triangle.SSA (side-side-angle) - having the lengths of two sides and a non-included angle (an angle that is not between the two), you can solve the whole triangle.SAS (side-angle-side) - having the lengths of two sides and the included angle (the angle between the two), you can calculate the remaining angles and sides, then use the SSS rule.SSS (side-side-side) - you basically have all three sides, from which you can calculate the angles, and from there - the height, using the Pythagorean theorem.So, how to calculate the area of a triangle using more advanced rules? You can solve the whole triangle starting from different sets of measurements:
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