# Plane and Spherical Trigonometry

Ginn & Company, 1894

### Contents

 Section 1 1 Section 2 3 Section 3 16 Section 4 28 Section 5 50 Section 6 71
 Section 7 89 Section 8 103 Section 9 136 Section 10 153 Section 11 1

### Popular passages

Page 96 - V-- 7. Prove that the sides of any plane triangle are proportional to the sines of the angles opposite to these sides. If 2s = the sum of the three sides (a, b, c) of a triangle, and if A be the angle opposite to the side a, prove that 2 _ 8. Prove that in any plane triangle C* ~~i
Page 23 - From the top of a hill the angles of depression of two objects situated in the...
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 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 109 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
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 143 - A very simple relation exists between the hour angle of the sun and the local (apparent) time of day. Since the hourly rate at which the sun appears to move from east to west is 15°, and it is Apparent noon when the sun is on the meridian of a place, it is evident that if hour angle = 0°, 15°, — 15°, etc., time of day is noon, 1 o'clock pM, 11 o'clock AM, etc. In general, if...
Page 142 - For (Fig. 46) the angle ZOB between the zenith of the observer and the celestial equator is obviously equal to his latitude, and the angle POZ is the complement of ZOB. The arc NP being the complement of PZ, it follows that the altitude of the elevated pole is equal to the latitude of the place of observation. The triangle ZPM then (however much it may vary in shape for different positions of the star M ), always contains the following five magnitudes : PZ— co-latitude of observer = 90°...