Plane and Spherical Trigonometry, Surveying and Tables |
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ABCD acute angle altitude angle of depression angle of elevation azimuth bearing centre chains circle colog cologarithm column compass computed cosine csc b csc divided east equal equation EXERCISE feet Find the angle Find the area Find the distance Find the height Find the value formulas functions Given Hence horizontal plane hour angle hypotenuse included angle length log cot log log csc log sec log tan log logarithm loge longitude mantissa measured meridian miles Napier's Rules observer obtain opposite parallel perpendicular plot Polaris pole position Quadrant radians radius regular polygon right angle right spherical triangle right triangle ship sails sides sight sin b sin sin x sin² sine solution star station subtended surface tan² tangent trigonometric functions Trigonometry vernier vertical whence
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Page 50 - ... y) = sin x' cos y + cos x' sin y, cos (x' + y) = cos x' cos y — sin x
Page 61 - 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 24 - 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 83 - A pole is fixed on the top of a mound, and the angles of elevation of the top and the bottom of the pole are 60° and 30° respectively.
Page 116 - For, 2Р = (а")' = а"г. . • . loga (N") = np=plog„N. 7. The logarithm of the real positive value of a root of a positive number is found by dividing the logarithm of the number by the index of the root.
Page 172 - 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 28 - From the top of a hill the angles of depression of two objects situated in the...
Page 50 - ... cos y + cos x sin y cos x cos y — sin x sin y tan a- + tan y 1 — tan x tan y sin (x — y) = sin x cos y — cos x...
Page 115 - Any positive number being selected as a base, the logarithm of any other positive number is the exponent of the power to which the base must be raised to produce the given number. Thus, if a
Page ii - If the number is less than 1 , make the characteristic of the logarithm negative, and one unit more than the number of zeros between the decimal point and the first significant figure of the given number.