# Plane and Spherical Trigonometry

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15. lappuse - The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side.
73. lappuse - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
73. lappuse - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
24. lappuse - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A =  cos B...
xi. lappuse - Prove that the square of any side of a triangle is equal to the sum of the squares of the other two sides diminished by twice the rectangle of these sides multiplied by the cosine of their included angle.
93. lappuse - From a station B at the base of a mountain its summit A is seen at an elevation of 60°; after walking one mile towards the summit up a plane making an angle of 30° with the horizon to another station C, the angle BCA is observed to be 135°.
27. lappuse - Trig. [19]), cos \ (A ± B) = cos \ A cos \ B ^ sin \ A sin \ B, the...
7. lappuse - The sine of any middle part is equal to the product of the tangents of the Adjacent parts. RULE II. The sine of any middle part is equal to the product of the cosines of the opposite parts.