Trigonometrical Formulæ.
To compute the Sides of Triangles.—Let A B C 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 θ the included angle,
A = a b sin. θ2.
To find by logarithms the area in acres and decimals of an acre,
Log. A = log. a + log. b + log. sin. θ - 15·30103.
When two angles and the included side are known, β and θ being the angles and a the included side,