Plane trigonometry, by S.L. Loney.

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RIGHT-ANGLED TRIANGLE. 16
Let b be the given side and c the given hypothenuse.
The angle B is given by the
relation A
sin B = - b.. Lsin B = 10 + log b- log c. B
Since b and c are known we
thus have L sin B and therefore B.
The angle A (= 90~ - B) is then known.
The side a is obtained from either of the relations
at b
cos B=-, tan B = -, or a = (c - b) (c + b).
c a
176. Case II. Given the two sides a and b, to solve
the triangle.
Here B is given by A
tanB =, b
a b
so that
L tan B = 10 + log b - log a. a
Hence L tan B, and therefore B, is known.
The angle A (= 90 - B) is then known.
The hypothenuse c is given by the relation c = /a2 +b2.
This relation is not however very suitable for logarithmic calculation, and c is best given by
b b
sinB =- i.e. c=.
c sin B.. log c = log b - log sin B
= 10 + log b - L sin B.

Hence c is obtained.