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{"sheet":"Instructions","index":0,"n_rows":20,"n_cols":4,"rows_kept":20,"cut":false,"hidden":false,"merged":[]}
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[null,"Trigonometry",null,"Sine and Cosine rules"]
[]
[null,"Step 1","Type any known values of angles or sides into the triangle on the left.  Change the level of accuracy in decimal places as required.  "]
[null,"Step 2","Click \"Apply New\" to feed these values into the calculator.  They should be mirrored (in grey) on the right-hand triangle.  "]
[null,"Step 3","Decide which function (listed between the two triangles) to apply, and click it.  If any new values can be found, these will show up in red.  "]
[null,"Step 4","Repeat the process, choosing which process to apply each time.  The four different processes available are:"]
[null,null,1,"Apply the Sine Rule"]
[null,null,2,"Apply the Cosine Rule"]
[null,null,3,"Calculate the Area"]
[null,null,4,"Find the Third Angle"]
[]
[null,"Note","Since the diagram doesn't change, it will rarely resemble the actual triangle, but results, where calculated, will be accurate.  "]
[null,null,"The sheet is protected to avoid accidental changes.  You can move between editable cells by pressing Tab.  "]
[null,null,"To unprotect the sheet for any reason, right click on the sheet tab and click 'Unprotect sheet'.  There is no password.  "]
[]
[null,"Also note:","This calculator only takes into account principle values, which means that - where possible - the ambiguous case is not"]
[null,null,"given.  It is worth noting that unless the information provided is sufficient to uniquely define a triangle (using congruency"]
[null,null,"conditions SSS, SAS, ASA or RHS), there may be two possible - equally valid - triangles generated.  This is mentioned"]
[null,null,"briefly at GCSE, but investigated more fully at A-level.  "]

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[null,null,null,null,null,null,null,null,null,null,"Sine and Cosine Rules\nClick a formula to apply the rule.  "]
[null,null,null,null,null,"Accuracy:",null,2,"d.p."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(S4=\"\",\"\",\"Area:\")","v":""}]
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[null,null,null,null,null,null,null,null,"A",null,null,"c",null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(C28=\"\",\"\",ROUND(C28,H2))","v":""},null,null,{"$f":"IF(C24=\"\",\"\",ROUND(C24,H2))","v":""}]
[null,null,null,null,"b",null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(C23=\"\",\"\",ROUND(C23,H2))","v":3}]
[]
[null,null,null,null,null,null,null,null,null,null,null,"B",null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(C26=\"\",\"\",ROUND(C26,H2))","v":30}]
[null,null,null,null,null,"C",null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(C27=\"\",\"\",ROUND(C27,H2))","v":""}]
[null,null,null,null,null,null,null,null,null,"a",null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(C25=\"\",\"\",ROUND(C25,H2))","v":5}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"180°"]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,"Sine rule:"]
[null,null,null,null,null,null,null,"Cos",null,"Angles in tri",null,null,null,null,"COPY to Apply"]
[null,null,null,null,"2 sides and incl angle",null,null,null,null,null,null,{"$f":"IF(L23=\"\",IF(L24=\"\",IF(L25=\"\",\"\",L25),L24),L23)","v":6.0000000000000009},"using it:",null,"Sine","Angles","Cosine",null,null,"inputs:"]
[3,"Side a",3,null,"Area",null,null,{"$f":"IF(C23=\"\",IF(OR(C24=\"\",C25=\"\",C26=\"\"),\"\",SQRT(C24^2+C25^2-2*C24*C25*COS(C26*PI()/180))),C23)","v":3},null,null,"a/sinA",{"$f":"IF(OR(C23=\"\",C26=\"\"),\"\",C23/SIN(C26*PI()/180))","v":6.0000000000000009},{"$f":"IF(C23=\"\",IF(C26=\"\",\"\",IF(L22=\"\",\"\",SIN(C26*PI()/180)*L22)),\"\")","v":""},null,{"$f":"IF(C23=\"\",IF(M23=\"\",\"\",M23),C23)","v":3},{"$f":"IF(C23=\"\",\"\",C23)","v":3},{"$f":"IF(C23=\"\",IF(H23=\"\",\"\",H23),C23)","v":3},null,null,{"$f":"IF(E6=\"\",\"\",E6)","v":"b"}]
["","Side b","",null,{"$f":"IF(E25=\"\",IF(E26=\"\",IF(E27=\"\",\"\",E27),E26),E25)","v":""},null,null,{"$f":"IF(C24=\"\",IF(OR(C25=\"\",C23=\"\",C27=\"\"),\"\",SQRT(C25^2+C23^2-2*C25*C23*COS(C27*PI()/180))),C24)","v":""},null,null,"b/sinB",{"$f":"IF(OR(C24=\"\",C27=\"\"),\"\",C24/SIN(C27*PI()/180))","v":""},{"$f":"IF(C24=\"\",IF(C27=\"\",\"\",IF(L22=\"\",\"\",SIN(C27*PI()/180)*L22)),\"\")","v":""},null,"",{"$f":"IF(C24=\"\",\"\",C24)","v":""},"",null,null,{"$f":"IF(L5=\"\",\"\",L5)","v":"c"}]
[5,"Side c",5,null,{"$f":"IF(OR(C23=\"\",C24=\"\",C28=\"\"),\"\",0.5*C23*C24*SIN(C28*PI()/180))","v":""},null,null,{"$f":"IF(C25=\"\",IF(OR(C23=\"\",C24=\"\",C28=\"\"),\"\",SQRT(C23^2+C24^2-2*C23*C24*COS(C28*PI()/180))),C25)","v":5},null,null,"c/sinC",{"$f":"IF(OR(C25=\"\",C28=\"\"),\"\",C25/SIN(C28*PI()/180))","v":""},{"$f":"IF(C25=\"\",IF(C28=\"\",\"\",IF(L22=\"\",\"\",SIN(C28*PI()/180)*L22)),\"\")","v":""},null,5,{"$f":"IF(C25=\"\",\"\",C25)","v":5},5,null,null,{"$f":"IF(J10=\"\",\"\",J10)","v":"a"}]
[30,"Angle A",30,null,{"$f":"IF(OR(C24=\"\",C25=\"\",C26=\"\"),\"\",0.5*C24*C25*SIN(C26*PI()/180))","v":""},null,null,{"$f":"IF(C26=\"\",IF(OR(C23=\"\",C24=\"\",C25=\"\"),\"\",ACOS((C24^2+C25^2-C23^2)/(2*C24*C25))*180/PI()),C26)","v":30},null,{"$f":"IF(C26=\"\",IF(OR(C27=\"\",C28=\"\"),\"\",180-C27-C28),C26)","v":30},null,null,{"$f":"IF(C26=\"\",IF(C23=\"\",\"\",IF(L22=\"\",\"\",ASIN(C23/L22)*180/PI())),\"\")","v":""},null,30,{"$f":"IF(J26=\"\",\"\",J26)","v":30},30,null,null,{"$f":"IF(L8=\"\",\"\",L8)","v":"B"}]
["","Angle B","",null,{"$f":"IF(OR(C25=\"\",C23=\"\",C27=\"\"),\"\",0.5*C25*C23*SIN(C27*PI()/180))","v":""},null,null,{"$f":"IF(C27=\"\",IF(OR(C24=\"\",C25=\"\",C23=\"\"),\"\",ACOS((C25^2+C23^2-C24^2)/(2*C25*C23))*180/PI()),C27)","v":""},null,{"$f":"IF(C27=\"\",IF(OR(C28=\"\",C26=\"\"),\"\",180-C28-C26),C27)","v":""},null,null,{"$f":"IF(C27=\"\",IF(C24=\"\",\"\",IF(L22=\"\",\"\",ASIN(C24/L22)*180/PI())),\"\")","v":""},null,"",{"$f":"IF(J27=\"\",\"\",J27)","v":""},"",null,null,{"$f":"IF(F9=\"\",\"\",F9)","v":"C"}]
["","Angle C","",null,null,null,null,{"$f":"IF(C28=\"\",IF(OR(C25=\"\",C24=\"\",C23=\"\"),\"\",ACOS((C24^2+C23^2-C25^2)/(2*C24*C23))*180/PI()),C28)","v":""},null,{"$f":"IF(C28=\"\",IF(OR(C27=\"\",C26=\"\"),\"\",180-C27-C26),C28)","v":""},null,null,{"$f":"IF(C28=\"\",IF(C25=\"\",\"\",IF(L22=\"\",\"\",ASIN(C25/L22)*180/PI())),\"\")","v":56.442690238079287},null,56.442690238079287,"","",null,null,{"$f":"IF(I5=\"\",\"\",I5)","v":"A"}]

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