Plane trigonometry, by S.L. Loney.

[Exs. LXVI.] ERRORS OF OBSERVATION.

467

13. The three sides of a triangle are measured and found to be
nearly equal. If the measurements can be wrong one per cent. in excess
or defect, prove that the greatest error that can arise in calculating one
of the angles is 80' nearly.
14. It is observed that the elevation of the summit of a mountain at
each corner of a plane horizontal equilateral triangle is a; prove that the
height of the mountain is
1
- a tan a,
V3
where a is the side of the triangle. If there be a small error n" in the
elevation at C, shew that the true height is
1 t 1 [~ insin" ]
/3 a tan 3 sin a cos a

30-2