The Draughtsman's Handbook of Plan and Map Drawing / Including instructions for the preparation of engineering, architectural, and mechanical drawings.

Trigonometrical FormulAE.

To compute the Sides of Triangles.—Let ABC be the angles of a plane triangle, and a b c the sides opposite. Then, for right-angled triangles, we have

b = a sin. B	or
b = c tan. B		b = c cot. C
c = a cos. B		c = b cot. B
c = b tan. C

and for oblique-angled triangles we have

b = a sin. Bsin. A,
c = a sin. Csin. A.

To compute the Areas of Triangles.—When two sides and the included angle are known, a and b representing the two sides and ? the included angle,

A = a b sin. ?2.

To find by logarithms the area in acres and decimals of an acre,

Log. A = log. a + log. b + log. sin. ? - 15·30103.

When two angles and the included side are known, and ? being the angles and a the included side,

A = a² sin. sin. ?2 sin. ( + ?).

To find by logarithms the area in acres and decimals of an acre,

Log. A = 2 log. a + log. sin. + log. sin. ? - log. sin. ( + ?) - 15·30103.

When the three sides are known, a b c being the three sides and s their half sum,

A = vs(s - a)(s - b)(s - c).

To find by logarithms the area in acres and decimals of an acre,

Log. A = log. s + log. (s - a) + log. (s - b) + log. (s - c)2 - 5.

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