How to Compute the Angles in an Obtuse Triangle
An obtuse triangle has one angle that is more than 90 degrees. Determining how much more than 90 degrees it is and calculating the measurement of the other angles involves trigonometry. To compute all three angles in an obtuse triangle, you must know the lengths of all the sides. Once you know this, you can use the Law of Cosines to solve for the first two angles, then subtract the sum of these angles from 180 degrees -- the total of all the angles in any triangle -- to calculate the last side.
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Instructions
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Substitute the lengths of the sides into the Law of Cosines equation: a^2 + b^2 - (2ab)cos(C) = c^2. For instance, a triangle has sides labeled a, b and c, such that a = 5 cm, b = 3 cm and c = 7 cm. When you substitute these values into the Law of Cosines, the resulting equation looks like this: 5^2 + 3^2 - 2(5)(3)cos(C) = 7^2
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Simplify the equation. For instance, 5^2 + 3^2 - 2(5)(3)cos(C) = 7^2 becomes 25 + 9 - 30cos(C) = 49, which simplifies to 34 - 30cos(C) = 49.
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Rearrange the equation to isolate the unknown angle, C. Rearranged, the equation becomes cos(C) = (34 - 49)/30, or cos(C) = -0.5
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Take the inverse cosine, or arccosine (acos), of both sides to solve for C. Angle C equals 120 degrees.
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Repeat this process to find the second angle, using one of the two modified Law of Cosines equations: b^2 + c^2 - (2bc)cos(A) = a^2 or a^2 + c^2 - (2ac)cos(B) = b^2. For instance, angle "A" equals 38.21 degrees.
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Add the two known angles together and subtract this answer from 180 degrees to find the measure of the last angle. For example, 120 + 38.21 = 158.21. 180 - 158.21 = 21.79. Therefore, angle "A" measures 21.79 degrees.
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