he angle between the two known sides).","points":1},{"id":"14e3bc6d-8e2f-41ab-8fa4-c60f564046ce","cardType":"basic","front":"What information is required to use the Cosine Rule to find a missing angle?","back":"The lengths of all three sides.","points":1},{"id":"4b131bd4-87ac-4bf0-8341-9edb40de10fb","cardType":"cloze","front":"In the formula $a^2 = b^2 + c^2 - 2bc\\cos A$, side $\\text{[...]}$ must be opposite angle $A$.","back":"In the formula $a^2 = b^2 + c^2 - 2bc\\cos A$, side $\\boxed{a}$ must be opposite angle $A$.","points":null},{"id":"55e4bdf9-4955-4b14-89af-d36dbe97ceb3","cardType":"cloze","front":"In the formula $a^2 = b^2 + c^2 - 2bc\\cos A$, side $a$ must be opposite [ ].","back":"In the formula $a^2 = b^2 + c^2 - 2bc\\cos A$, side $a$ must be opposite angle $A$.","points":null},{"id":"2023db3a-5924-4fc7-86b0-2fbd7b3d525a","cardType":"basic","front":"In triangle $ABC$, which side is opposite angle $C$?","back":"Side $AB$.","points":1},{"id":"ec15507e-c080-4721-9e79-47cdcb853054","cardType":"cloze","front":"To find a missing side $a$, the Cosine Rule is: $$\\text{[...]}$$","back":"To find a missing side $a$, the Cosine Rule is: $$\\boxed{a^2 = b^2 + c^2 - 2bc\\cos A}$$","points":null},{"id":"a557d571-3193-4413-bc73-d4cfffaa3fde","cardType":"basic","front":"Why is the Cosine Rule used instead of Pythagoras or SOHCAHTOA?","back":"It works for non-right-angled triangles.","points":1},{"id":"740f2816-ea34-418b-8b39-3e06870b87a5","cardType":"basic","front":"What is the final step when calculating a missing side length using $a^2 = b^2 + c^2 - 2bc\\cos A$?","back":"Take the square root of the result.","points":1},{"id":"2d16136d-c7db-406f-98d3-6ee9906f6026","cardType":"basic","front":"What setting must your calculator be in for GCSE triangle trigonometry?","back":"Degrees mode.","points":1},{"id":"22c0b45b-c66e-44b9-8eb1-824029eaffa4","cardType":"cloze","front":"The rearranged Cosine Rule to find angle $A$ is: $$\\text{[...]}$$","back":"The rearranged Cosine Rule to find angle $A$ is: $$\\boxed{\\cos A = \\frac{b^2 + c^2 - a^2}{2bc}}$$","points":null},{"id":"59831ec9-0603-4188-b69d-a542b759c3cd","cardType":"basic","front":"When finding a missing angle, which side length is subtracted in the numerator of the formula?","back":"The side opposite the missing angle.","points":1},{"id":"9f989a41-d408-4815-ba23-5dc9be6caf1b","cardType":"basic","front":"How do you calculate the actual angle value once you know the value of $\\cos A$?","back":"Use the inverse cosine function ($\\cos^{-1}$).","points":1},{"id":"637bb021-899a-4233-a6c0-58f3252f876b","cardType":"basic","front":"If side lengths are given as algebraic expressions (e.g. $x+1$), what type of equation is often formed using the Cosine Rule?","back":"A quadratic equation.","points":1},{"id":"36a1d2da-73b9-407d-a240-a79afc778492","cardType":"basic","front":"Why should a solution like $x = -6$ be rejected when solving for algebraic side lengths?","back":"Side lengths cannot be negative.","points":1},{"id":"2e308d75-760f-4f36-9d4e-ad7d1b5db040","cardType":"cloze","front":"The formula for the area of a triangle using two sides and an included angle is: $$\\text{[...]}$$","back":"The formula for the area of a triangle using two sides and an included angle is: $$\\boxed{\\text{Area} = \\frac{1}{2}ab\\sin C}$$","points":null},{"id":"ce574a7b-00af-45bd-bc21-9c45a8aeb76a","cardType":"basic","front":"What are the 3 steps to find the perimeter of a triangle given two sides and its area?","back":"

Use the Area formula to find the included angle
Use the Cosine Rule to find the third side

The Cosine Rule Flashcards

The Cosine Rule Flashcards

The Cosine Rule Flashcards

The Cosine Rule Flashcards