Question #124228
A ladder AB which is setup with B on the horizontal ground and A against a vertical wall, makes an angle of 71 degrees with the ground. it is prevented from slipping by a tight rope PQ of length 1.68 metres, fixed at P to the foot of the wall and at Q to the ladder, PQ being at right angles to AB. Calculate in centimetres
a) The height AP of the ladder above P
b) The length of the ladder?
1
Expert's answer
2020-06-29T15:53:28-0400

As per the question,ABP=QPA=71°\angle ABP = \angle QPA= 71\degree


PQ=1.68 mPQ=1.68\ m

a) PQAP=cos 71°    \frac{PQ}{AP}=cos \ 71\degree\implies

AP=PQcos 71°=1.680.325=5.16 mAP=\frac{PQ}{cos \ 71\degree}=\frac{1.68}{0.325}= 5.16\ m

b) APAB=sin 71°    AB=APsin71°=5.160.945=5.46 m\frac{AP}{AB}=sin \ 71\degree \implies AB= \frac{AP}{sin 71\degree}= \frac{5.16}{0.945}=5.46\ m




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