Plane trigonometry, by S.L. Loney.

HEIGHTS AND DISTANCES.

211

AP sinPBA siny
Hence - =
Hence a sin BPA sin (/ + y)
From the triangle PAQ, we have
sin a sin y
x = AP sin a = a.
sin (3 +y)'
Hence x is found by an expression suitable for
logarithmic calculation.
194. To find the distance between two inaccessible points
by means of observations made at two points the distance
between which is known, all four points being supposed to
be in one plane.
Let P and Q be two points whose distance apart, PQ,
is required.
Let A and B be the two known
points whose distance apart, AB, is
given to be equal to a.
At A measure the angles PAB
and QAB, and let them be a and 3 A ' — B
respectively.
At B measure the angle PBA and QBA, and let them
be ry and 8 respectively.
Then in the triangle PAB we have one side a and the
two adjacent angles a and 7 given, so that, as in Art. 163,
we have AP given by the relation
AP sin 7 sin 7
P sin APB- sin (a + 7).........
In the triangle QAB we have, similarly,
AQ sin 8
a sin (3+) ).............
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