![]() We extend the base as shown and determine the height of the obtuse triangle.Īrea of ΔABC = 1/2 × h × b where BC is the base, and h is the height of the triangle.Īrea of an Obtuse-Angled Triangle = 1/2 × Base × Height Obtuse Triangle Area by Heron's Formula The altitude or the height from the acute angles of an obtuse triangle lies outside the triangle. In the given obtuse triangle ΔABC, we know that a triangle has three altitudes from the three vertices to the opposite sides. Once the height is obtained, we can find the area of an obtuse triangle by applying the formula mentioned below. Since an obtuse triangle has a value of one angle more than 90°. ![]() To find the area of an obtuse triangle, a perpendicular line is constructed outside of the triangle where the height is obtained. Perimeter of obtuse-angled triangle = (a + b + c) units. Hence, the formula for the perimeter of an obtuse-angled triangle is: The perimeter of an obtuse triangle is the sum of the measures of all its sides. Let's learn each of the formulas in detail. There are separate formulas to calculate the perimeter and the area of an obtuse triangle. Therefore, it is called an obtuse-angled triangle or simply an obtuse triangle. The triangle below has one angle greater than 90°. Centroid and incenter lie within the obtuse-angled triangle while circumcenter and orthocenter lie outside the triangle. Therefore, a right-angle triangle cannot be an obtuse triangle and vice versa. Similarly, a triangle cannot be both an obtuse and a right-angled triangle since the right triangle has one angle of 90° and the other two angles are acute. Hence, the triangle is an obtuse-angled triangle where a 2 + b 2 < c 2Īn obtuse-angled triangle can be a scalene triangle or isosceles triangle but will never be equilateral since an equilateral triangle has equal sides and angles where each angle measures 60°. For example, in a triangle ABC, three sides of a triangle measure a, b, and c, c being the longest side of the triangle as it is the opposite side to the obtuse angle. The side opposite to the obtuse angle is considered the longest. if one of the angles measure more than 90°, then the sum of the other two angles is less than 90°. An obtuse-angled triangle has one of its vertex angles as obtuse and other angles as acute angles i.e. We also use inverse cosine called arccosine to determine the angle from the cosine value.An obtuse-angled triangle or obtuse triangle is a type of triangle whose one of the vertex angles is bigger than 90°. With the Law of Cosines, there is also no problem with obtuse angles as with the Law of Sines because the cosine function is negative for obtuse angles, zero for right, and positive for acute angles. It is best to find the angle opposite the longest side first. Pythagorean theorem is a special case of the Law of Cosines and can be derived from it because the cosine of 90° is 0. Pythagorean theorem works only in a right triangle. The Law of Cosines extrapolates the Pythagorean theorem for any triangle. The cosine rule, also known as the Law of Cosines, relates all three sides of a triangle with an angle of a triangle. ![]() Calculation of the inner angles of the triangle using a Law of CosinesThe Law of Cosines is useful for finding a triangle's angles when we know all three sides.
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