Plane and Spherical Trigonometry

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Ginn, 1876 - 163 sider
 

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Side 22 - 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...
Side 73 - 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.
Side xi - 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.
Side 94 - At a second station, bearing from the first N. by E., and distant 1 mile, the bearing of the cloud is W. by N. Find the height of the cloud, and its distance from each station. Ans. 7727 feet...
Side 93 - 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° : find the height of the mountain in yards.
Side 23 - Oblique spherical triangle sin a sin b sin c Sine Law: —• — T- = -i — B = ~ — T=\ sin A sin B sin C Cosine Law: cos a = cos b cos c + sin b sin c...
Side 39 - The hour angle of a heavenly body is the inclination of the hour circle (circle of declination) which passes through the body to the celestial meridian, and is measured by the arc of the celestial equator...
Side 22 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.

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