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 cos² cosine csc A 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 longitude mantissa measured meridian miles Napier's Rules observer obtain opposite perpendicular plot Polaris pole position Quadrant radians radius regular polygon right angle right ascension right spherical triangle right triangle ship sails sides sin a sin sin² sine solution star station surface tan² tangent trigonometric functions Trigonometry vernier vertical whence
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Page 62 - a 2 + c 2 — 2 ac cos B, The three formulas have precisely the same form, and the law may be stated as follows : The square of any side of a triangle is equal to the sum of the squares of the other two sides., diminished by
Page 61 - The sides of a triangle are proportional to the sines of the opposite angles. If we regard these three equations as proportions, and take them by alternation, it will be evident that they may be written in the symmetrical form,
Page 117 - VI. CONSTRUCTION OP TABLES. § 42. LOGARITHMS. Properties of Logarithms. 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
Page 118 - np = p log a 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. For,
Page 93 - 180 ° 4 n 103. The area of a regular polygon inscribed in a circle is to that of the circumscribed polygon of the same number of sides as 3 to 4. Find the number of sides. 104. The area of a regular polygon inscribed in a circle is a
Page 73 - that is, the case in which the triangle is isosceles. 14. If two sides of a triangle are 10 and 11, and the included angle is 50°, find the third side. 15. If two sides of a triangle are 43.301 and 25, and the included angle is 30°, find the third side. distances
Page 64 - C = 180°, are sufficient for solving every case of an oblique triangle. The three parts that determine an oblique triangle may be : I. One side and two angles ; II. Two sides and the angle opposite to one of these sides ; III. Two sides and the included angle ; IV. The three sides. Let
Page 162 - 59. CASE IV. Given two angles A and B, and the side, a opposite to one of them. The side b is found from [44], whence sin b = sin a sin B esc A. The values of c and C may then be found by means of Napier's Analogies, the fourth and second of which give
Page iii - Therefore, log A n — an = n log A. 5. The logarithm of the root of a number is found by dividing the logarithm of the number by the index of the root. For, -\/Z
Page 95 - by E. f E., until the departure is 207 miles. Find the distance, and the latitude reached. 114. A ship sails on a course between S. and E., 244 miles, leaving latitude 2° 52' S., and reaching latitude 5° 8' S. Find the course, and the departure. 115. A ship sails from latitude 32° 18