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["The Cosine Rule for Angles"]
[null,"Work out all the angles when you know all three sides"]
[]
[null,"Side a",null,"Side b",null,"Side c"]
[null,null,null,null,null,null,null,"units do not matter, so long as all three lengths are in the same units"]
[]
[null,"Angle opposite side a",null,"Angle opposite side b",null,"Angle opposite side c",null,"Area of Triangle",null,null,{"$f":"IF(OR(ISBLANK(B5),ISBLANK(D5),ISBLANK(F5),B10=\"impossible\",D10=\"impossible\",F10=\"impossible\"),\"\",\"Check: TOTAL OF THREE ANGLES\")","v":""}]
[null,{"$f":"IF(OR(ISBLANK($B$5),ISBLANK($D$5),ISBLANK($F$5)),\"\",(b^2+d^2-a^2)/(2*b*d))","v":""},null,{"$f":"IF(OR(ISBLANK($B$5),ISBLANK($D$5),ISBLANK($F$5)),\"\",(a^2+d^2-b^2)/(2*a*d))","v":""},null,{"$f":"IF(OR(ISBLANK($B$5),ISBLANK($D$5),ISBLANK($F$5)),\"\",(b^2+a^2-d^2)/(2*b*a))","v":""}]
[null,{"$f":"IF(OR(ISBLANK($B$5),ISBLANK($D$5),ISBLANK($F$5)),\"\",CONCATENATE(\"=\",b^2+d^2-a^2,\"/\",2*b*d))","v":""},null,{"$f":"IF(OR(ISBLANK($B$5),ISBLANK($D$5),ISBLANK($F$5)),\"\",CONCATENATE(\"=\",a^2+d^2-b^2,\"/\",2*a*d))","v":""},null,{"$f":"IF(OR(ISBLANK($B$5),ISBLANK($D$5),ISBLANK($F$5)),\"\",CONCATENATE(\"=\",b^2+a^2-d^2,\"/\",2*b*a))","v":""}]
[null,{"$f":"IF(OR(ISBLANK($B$5),ISBLANK($D$5),ISBLANK($F$5)),\"\",IF(ISERROR(DEGREES(ACOS((b^2+d^2-a^2)/(2*b*d)))),\"impossible\",DEGREES(ACOS((b^2+d^2-a^2)/(2*b*d)))))","v":""},null,{"$f":"IF(OR(ISBLANK($B$5),ISBLANK($D$5),ISBLANK($F$5)),\"\",IF(ISERROR(DEGREES(ACOS((a^2+d^2-b^2)/(2*a*d)))),\"impossible\",DEGREES(ACOS((a^2+d^2-b^2)/(2*a*d)))))","v":""},null,{"$f":"IF(OR(ISBLANK($B$5),ISBLANK($D$5),ISBLANK($F$5)),\"\",IF(ISERROR(DEGREES(ACOS((b^2+a^2-d^2)/(2*b*a)))),\"impossible\",DEGREES(ACOS((b^2+a^2-d^2)/(2*b*a)))))","v":""},null,{"$f":"IF(OR(ISBLANK($B$5),ISBLANK($D$5),ISBLANK($F$5)),\"\",a*b*SIN(RADIANS(F10))/2)","v":""},null,null,{"$f":"IF(OR(ISBLANK(B5),ISBLANK(D5),ISBLANK(F5),B10=\"impossible\",D10=\"impossible\",F10=\"impossible\"),\"\",B10+D10+F10)","v":""}]
[]
[]
[]
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