## Plane and Spherical Trigonometry |

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acute angle angle applied base becomes called centre circle circular colog column complement complete computation Construct correction corresponding cosine cotangent denote determined difference direction distance equal equation Example expression feet figures find the functions formulas four geometry give Given greater Hence horizon hypothenuse increase initial line interpolation length less letter logarithm manner measure method miles negative observer obtained opposite perpendicular plane positive possible principle problems proportional Prove Putting quadrant radius ratios regard relations represent respectively right triangle rule secant sides sin a sin sine solution solve spherical student substituting tabulated taken tangent terminal line third tions trigonometric functions unit unity

### Popular passages

Page xi - 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.

Page 91 - 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°.

Page 20 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.

Page 73 - 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.

Page 46 - By [2]. [18]. and [19]. we have. — sin (a ± ß) sin a cos ß ± cos a sin ß cos (a ± ß) cos acoeß Т sin a sin ß Divide both numerator and denominator by cos a cos |3.

Page 69 - Having measured a distance of 200 feet, in a direct horizontal line, from the bottom of a steeple, the angle of elevation of its top, taken at that distance, was found to be 47° 30'; from hence it is required to find the height of the steeple.