Plane trigonometry, by S.L. Loney.

210

TRIGONOMETRY.

From the triangle PBQ we have
BP5111I3.(1),
Bp sin,3.......................(1),
and from the triangle PAB we have
PB sin PAB sin a
(2),
a sinBPA sin(/3 -a)......
since L BPA = z QBP- z QAP =/3 -a.
From (1) and (2), by multiplication, we have
x sin a sin,/
a sin ( -a) '
sin a sin,
z.e. x=a.
sln (t a) '
The height x is therefore given in a form suitable for
logarithmic calculation.
Numerical Example. If a = 100 feet, a = 30~, and = 60~, then
- sin 300 sin 60~, J3
x=1 00 sin 60 = 100x3 -=86'6 feet.
sin 300 2
193. It is often not convenient to measure AB
directly towards Q.
Measure therefore AB in any
other suitable direction on the horizontal ground and at A measure the
angle of elevation a of P, and also A
Q-'
the angle PAB (=/3).
At B measure the angle PBA a
(= ). B
In the triangle PAB we have then

Z APB = 180~ - z PAB - z PBA = 180~ - (/8 + 7).