What is the angle?
Geometry
Level
2
In Right Angled Triangle ABC,Angle B =90 , AB=BC and P and Q are points on side AC such that PQ^2 =AP^2 +CQ^2.Then, Find Angle PBQ?
60
45
67.5
90
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1 solution
I will give you a hint,basically an algorithm.
area of {ABP +PBQ +QBC}=area of ABC
0.5 AB.BC= 0.5sin(ABP)AB BP + 0.5sin(PBQ)PB BQ+ 0.5sin(QBC)QB BC
Apply sine rule separately in triangle ABP,PBQ,QBC to find the value of AB.BP,PB.BQ,BQ.BC respectively.You plug the required values and you will get the value of sinPBQ=1/2^1/2