Plane and Spherical Trigonometry: G. A. Wentworth ...

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Ginn, 1884 - Trigonometry - 6460 pages
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Page 52 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.
Page 51 - The sides of a triangle are proportional to the sines of the opposite angles.
Page 52 - 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 product of the sides and the cosine of the included angle.
Page 23 - From the top of a hill the angles of depression of two successive milestones, on a straight level road leading to the hill, are observed to be 5 and 15. Find the height of the hill.
Page 77 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 53 - The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides.
Page 136 - Assuming the formula for the sine of the sum of two angles in terms of the sines and cosines of the separate angles, find (i.) sin 75 ; (ii.) sin 3 A in terms of sin A.
Page 20 - Geometry that the area of a triangle is equal to one-half the product of the base by the altitude. Therefore, if a and b denote the legs of a right triangle, and F the area...
Page 108 - Azimuth of a point in the celestial sphere is the angle at the zenith between the meridian of the observer and the vertical circle passing through the point; it may also be regarded as the arc of the horizon intercepted between those circles.
Page 133 - Write down the sines of all the angles which are multiples of 30 and less than 360.

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