Answer to Question #124228 in Trigonometry for Rume Ighoraye

Question

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?

Answer 1

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

$PQ=1.68\ m$

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

$AP=\frac{PQ}{cos \ 71\degree}=\frac{1.68}{0.325}= 5.16\ m$

b) $\frac{AP}{AB}=sin \ 71\degree \implies AB= \frac{AP}{sin 71\degree}= \frac{5.16}{0.945}=5.46\ m$