Two angles of the triangle are given. Find the third angle. Show 80°, 60° 80°, 60° Let the third angle be x Sum of the angles = 180° 80° + 60° + x = 180° 140 + x = 180° x = 180° − 140° x = 40° Third angle = 40° Concept: Triangle Inequality Is there an error in this question or solution? Page 2Two angles of the triangle are given. Find the third angle. 75°, 35° 75°, 35° Let the third angle be x Sum of the angles 180° 75° + 35° + x = 180° 110 + x = 180° x = 180° – 110° x = 70° Third angle = 70° Concept: Triangle Inequality Is there an error in this question or solution? Page 3Two angles of the triangle are given. Find the third angle. 52°, 68° 52°, 68° Let the third angle be x Sum of the angles = 180° 52° + 68° + x = 180° 120 + x = 180° x = 180° – 120° x = 60° Third angle = 60° Concept: Triangle Inequality Is there an error in this question or solution? Page 4Two angles of the triangle are given. Find the third angle. 50°, 90° 50°, 90° Let the third angle be x. Sum of the angles = 180° 50° + 90° + x = 180° 140 + x = 180° x = 180° – 140° x = 40° Third angle = 40° Concept: Triangle Inequality Is there an error in this question or solution? Page 5Two angles of the triangle are given. Find the third angle. 120°, 30° 120°, 30° Let the third angle be x Sum of the angles = 180° 120° + 30° + x = 180° 150 + x = 180° x = 180° – 150° x = 30° Third angle = 30° Concept: Triangle Inequality Is there an error in this question or solution? Page 6Two angles of the triangle are given. Find the third angle. 55°, 85° 55°, 85° Let the third angle be x Sum of the angles = 180° 55° + 85° + x = 180° 140 + x = 180° x = 180° – 140° x = 40° Third angle = 40° Concept: Triangle Inequality Is there an error in this question or solution?
"Solving" means finding missing sides and angles.
Six Different TypesIf you need to solve a triangle right now choose one of the six options below: Which Sides or Angles do you know already? (Click on the image or link) AAA Three Angles AAS Two Angles and a Side not between ASA Two Angles and a Side between SAS Two Sides and an Angle between SSA Two Sides and an Angle not between SSS Three Sides ... or read on to find out how you can become an expert triangle solver: Your Solving ToolboxWant to learn to solve triangles? Imagine you are "The Solver" ... In your solving toolbox (along with your pen, paper and calculator) you have these 3 equations:
A + B + C = 180° When you know two angles you can find the third. 2. Law of Sines (the Sine Rule):asin(A) = bsin(B) = csin(C) When there is an angle opposite a side, this equation comes to the rescue. Note: angle A is opposite side a, B is opposite b, and C is opposite c. 3. Law of Cosines (the Cosine Rule):c2 = a2 + b2 − 2ab cos(C) This is the hardest to use (and remember) but it is sometimes needed It is an enhanced version of the Pythagoras Theorem that works Six Different Types (More Detail)There are SIX different types of puzzles you may need to solve. Get familiar with them: 1. AAAThis means we are given all three angles of a triangle, but no sides. AAA triangles are impossible to solve further since there are is nothing to show us size ... we know the shape but not how big it is. We need to know at least one side to go further. See Solving "AAA" Triangles . 2. AASThis mean we are given two angles of a triangle and one side, which is not the side adjacent to the two given angles. Such a triangle can be solved by using Angles of a Triangle to find the other angle, and The Law of Sines to find each of the other two sides. See Solving "AAS" Triangles. 3. ASAThis means we are given two angles of a triangle and one side, which is the side adjacent to the two given angles. In this case we find the third angle by using Angles of a Triangle, then use The Law of Sines to find each of the other two sides. See Solving "ASA" Triangles . 4. SASThis means we are given two sides and the included angle. For this type of triangle, we must use The Law of Cosines first to calculate the third side of the triangle; then we can use The Law of Sines to find one of the other two angles, and finally use Angles of a Triangle to find the last angle. See Solving "SAS" Triangles . 5. SSAThis means we are given two sides and one angle that is not the included angle. In this case, use The Law of Sines first to find either one of the other two angles, then use Angles of a Triangle to find the third angle, then The Law of Sines again to find the final side. See Solving "SSA" Triangles . 6. SSSThis means we are given all three sides of a triangle, but no angles. In this case, we have no choice. We must use The Law of Cosines first to find any one of the three angles, then we can use The Law of Sines (or use The Law of Cosines again) to find a second angle, and finally Angles of a Triangle to find the third angle. See Solving "SSS" Triangles . Tips to SolvingHere is some simple advice: When the triangle has a right angle, then use it, that is usually much simpler. When two angles are known, work out the third using Angles of a Triangle Add to 180°. Try The Law of Sines before the The Law of Cosines as it is easier to use. Copyright © 2021 MathsIsFun.com |