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
Sum all three side lengths

","points":3},{"id":"10e79b4c-2191-4ed9-b962-5ca101fbb76c","cardType":"basic","front":"Why is it important to keep full calculator values until the final answer?","back":"To avoid rounding

The Cosine Rule Flashcards

The Cosine Rule Flashcards

The Cosine Rule Flashcards

The Cosine Rule Flashcards