How to Find Angles of Triangles
Triangles and angles are used in many everyday activities, including crafting, sewing, construction, roofing, architecture, and interior design. When any two lines meet at a point, they form an angle. Three lines coming together forming three points also form a triangle. All triangles have six parts, three angles and three sides. If you have the value of any three parts, you can find the value of the other three parts. Learning the basics is important in determining angles.
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Instructions
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How to Find Angles of Triangles
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Master the basic facts. Angles of triangles are measured in degrees. The three internal angles of a triangle equal 180°. An isosceles triangle has two equal sides, and the angles opposite those sides are equal. In an equilateral triangle all sides and angles are equal. A right triangle has one right angle, which is 90°. Acute triangles have three angles that are all less than 90°. Obtuse triangles have one angle that is greater than 90°.
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Learn the sine and cosine of an angle to solve the complex problems. Sine is a ratio between the opposite side and the hypotenuse side of a triangle. Sine = opposite side / hypotenuse side. Cosine is a ratio between the adjacent side and the hypotenuse side. Cosine = adjacent side / hypotenuse side.
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Know formulas and rules. Since all angles of a triangle must equal 180°, the first formula is A + B + C = 180°. The sine rule is: a / sin A = b / sin B = c / sin C. The final rule is the cosine rule: a² = b² + c² - 2bc cosA or b² = a² + c² -- 2ac cosB or c² = b² + a² -- 2ba cosC. Using these rules, you can find any angles or sides of a triangle as long as you have the value of three parts.
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Find the missing angles. When you know the value of two sides and one angle of the triangle, begin with the cosine rule to find the missing side. Next, find the smaller of the two missing angles using the sine rule. Once you have two of your three angles, use your formula to find the third angle.
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Solve for the missing angle by adding the two known angles. If angle A = 24° and angle B = 56°, then angle C = X. Add your given angles: 24° + 56° = 80°. Subtract the total: 180° -- 80° = 100°. Your missing angle is 100°. If you have the value of two of the angles, you can easily find the third.
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Tips & Warnings
A hypotenuse is only found in a right triangle.
Lower case letters refer to the sides and capital letters to the angles.
Change your triangle to a right triangle to find sine and cosine.
