Plane and Spherical Trigonometry

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Ginn, Heath & Company, 1882 - Trigonometry - 201 pages

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Page 109 - 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 51 - EXERCI8E XII. 1. What do the formulas of § 36 become when one of the angles is a right angle ? 2. Prove by means of the Law of Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Page 50 - 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 50 - 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 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...
Page 23 - From the top of a hill the angles of depression of two objects situated in the...
Page 104 - The vertical circle passing through the east and west points of the horizon is called the Prime Vertical; that passing through the north and south points coincides with the celestial meridian.
Page 68 - W., and after the ship had sailed 18 miles S. 67° 30' W. it bore N. 11° 15' E. Find its distance from each position of the ship. 2. Two objects, A and B, were observed from a ship to be at the same instant in a line bearing N. 15° E. The ship then sailed northwest 5 miles, when it was found that A bore due east and В bore northeast.
Page 53 - Two observers 15 miles apart on a plain, and facing each other, find that the angles of elevation of a balloon in the same vertical plane with themselves are 55° and 58°, respectively.
Page 75 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.

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