Problem $2$ CLOI $($PLO $1$ H$)$

A total station was positioned at point $P.$ The instrument was oriented to sight point $Q.$ The

instrument displayed an azimuth of $358{11}^{\text{'}}{16}^{\text{'}\text{'}}$ for line PQ $.$ The instrument was then made to

measure slope distance PQ as $887\mathrm{.}352$ m at a vertical angle of $11{25}^{\text{'}}{28}^{\text{'}\text{'}}.$ The instrument was

then turned clockwise horizontally such that pointed to point $R.$ The instrument displayed an

azimuth of $53{19}^{\text{'}}{38}^{\text{'}\text{'}}$ for line PR$.$ The instrument was then made to measure slope distance PR

as $1274\mathrm{.}765$ m at a vertical angle of $-11{05}^{\text{'}}{43}^{\text{'}\text{'}}.$

$($a$)$ Sketch the site to show relative positions of points P$,$ Q$,$ and R$.(1$ Point$).$

$($b$)$ Calculate vertical distance QR$.(2$ Points$).$

$($c$)$ Calculate horizontal distance QR$.(2$ Points$).$