[ { "problemTheory": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem", "solutionTheory": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Solution", "label": "OppositeLen", "description": "Given a triangle $0$1$2 right angled at $2, the distance $0$1 can be computed from the angle at $1 and the distance $1$2", "requiredFacts": [ { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pA", "label": "a", "tp": { "original": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "simplified": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" } }, "df": null }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pB", "label": "b", "tp": { "original": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "simplified": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" } }, "df": null }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pC", "label": "c", "tp": { "original": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" }, "simplified": { "uri": "http://mathhub.info/MitM/core/geometry?3DGeometry?point", "kind": "OMS" } }, "df": null }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pdistBC_v", "label": "pdist$1$2_v", "tp": { "original": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "simplified": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" } }, "df": null }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pdistBC", "label": "pdistt$1$2", "tp": { "original": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?DistanceFact?distanceFact", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pB", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pC", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pdistBC_v", "kind": "OMS" } ], "kind": "OMA" }, "simplified": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?DistanceFact?distanceFact", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pB", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pC", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pdistBC_v", "kind": "OMS" } ], "kind": "OMA" } }, "df": null }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pangleABC_v", "label": "pangleAt$0$1$2_v", "tp": { "original": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" }, "simplified": { "uri": "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit", "kind": "OMS" } }, "df": null }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pangleABC", "label": "pangle$0$1$2", "tp": { "original": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?AngleFact?angleFact", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pA", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pB", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pC", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pangleABC_v", "kind": "OMS" } ], "kind": "OMA" }, "simplified": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?AngleFact?angleFact", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pA", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pB", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pC", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pangleABC_v", "kind": "OMS" } ], "kind": "OMA" } }, "df": null }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pangleBCA", "label": "pangle$1$2$0", "tp": { "original": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?AngleFact?angleFact", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pB", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pC", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pA", "kind": "OMS" }, { "float": 90.0, "kind": "OMF" } ], "kind": "OMA" }, "simplified": { "applicant": { "uri": "http://mathhub.info/FrameIT/frameworld?AngleFact?angleFact", "kind": "OMS" }, "arguments": [ { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pB", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pC", "kind": "OMS" }, { "uri": "http://mathhub.info/FrameIT/frameworld?OppositeLen_Problem?pA", "kind": "OMS" }, { "float": 90.0, "kind": "OMF" } ], "kind": "OMA" } }, "df": null } ] } ]