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acute angle base bearing called circle column compass computed corresponding cosine departure determined difference direction distance divided draw east elevation equal equation EXAMPLE EXERCISE feet field figures Find the area formulas functions give Given height Hence horizontal hour known latitude length less log cos log cot log log sin log tan log logarithm mantissa means measured meridian method miles move negative NOTE object observer obtain opposite parallel passing perpendicular plane plot pole position PROBLEM Prove Quadrant radius reached regular represent respectively right triangle sails ship sides sight sine solution solve star station surface survey taken tangent tower Trigonometry turning unit vernier vertical whence
Page 141 - 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 68 - TJie area of a triangle is equal to half the product of two sides and the sine of the included angle.
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 53 - The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides.
Page 98 - 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 138 - 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 107 - II. The sine of the middle part is equal to the product of the cosines of the opposite parts.