Question $9.$

$[5$ Marks$]$

Trigonometrical heighting $($short distance$)$

The height at the end of an existing kerb is needed for the design of a road extension. The engineer sets up the total station at point A which has a height above datum of $48\mathrm{.}850$ m $.$ The following measurements are obtained:

Slope distance $=63\mathrm{.}028m$

Height of instrument at $A=1\mathrm{.}685m$

Zenith angle $=95{58}^{\text{'}}{20}^{\text{'}\text{'}}$

Height of reflector at end of kerb $=1\mathrm{.}400m$

$($a$)$ Calculate the horizontal distance from A to the end of the kerb

$($b$)$ Calculate the RL at the end of the kerb

Page $6$ of $7$

Question $10.$

$[10$ Marks$]$

Trigonometrical heighting $($long distance$)$

A surveyor needs a reduced level on Peg Y on the other side of a valley and he decides to establish this using vertical angles and an EDM slope distance. The surveyor sets up on Peg X on this side of the valley and obtains the following measurements:

$RLof$ Peg $x=63\mathrm{.}874mams{l}^{**}$ Slope distance $=778\mathrm{.}604m$

Instrument height $=1\mathrm{.}750$ Observed zenith angle $=87{21}^{\text{'}}{30}^{\text{'}\text{'}}$

Target height $=1\mathrm{.}550,R=6375km,k=0\mathrm{.}15$

amsl$-$abovemeanseallevel

$($a$)$ Calculate the horizontal distance between the instrument & target

$($b$)$ Calculate the RL of Peg Y $($the mark on the far side of the river where the target is located$)$