(Surveyor’s field angles)
(i) A surveyor records three angles as 0.785 rad, 1.0472 rad and 5.23599 rad. Convert each of these to degrees, minutes and seconds, rounding to the nearest second.
(ii) Compute the sum of the three angles:
(a) in radians (retain four decimal places),
(b) in degrees, minutes and seconds (nearest second).
(iii) State whether the sum exceeds a straight angle and, if so, by how many degrees and minutes.