## Plane and spherical trigonometry |

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acute angle altitude angle of elevation antilog apothem chord circle colog cologarithm computed cos2 cosecant cosine cosx cot2 cotangent Cotg decimal diagonal dihedral angle equal equation example Exercise figure Find antilog Find log find the angle Find the area Find the distance Find the length Find the numerical Find the value five-place tables formula four-place tables geometry given number Hence history of trigonometry hypotenuse isosceles triangle latitude law of sines Let the pupil log cot logarithms longitude mantissa measured method nautical miles numerical value oblique triangles obtained perpendicular Plane Trigonometry Prove radians radius Regiomontanus right angle right spherical triangle right triangle secant Similarly sin2 solution Solve in full solve the following solve the triangle Spherical Trigonometry statute miles subtends Subtract tan2 Tang tangent tower triangle ABC trigonometric functions

### Popular passages

Page 14 - To Divide One Number by Another, Subtract the logarithm of the divisor from the logarithm of the dividend, and obtain the antilogarithm of the difference.

Page 10 - 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.

Page 111 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.

Page 14 - To extract the required root of a number : Divide the logarithm of the number by the index of the required root and find the antilogarithm of the quotient.

Page 179 - At a point 200 feet from, and on a level with the base of a tower, the angle of elevation of the top of the tower is observed to be 60° : what is the height of the tower?

Page 107 - For example, if we have the angles of a plane triangle given, we know the ratios of the sides to each other, since the sides are to each other as the sines of the angles opposite ; but we cannot determine the abwlute values of the sides.

Page 21 - What is the side of a square whose area is equal to that of a circle 452 feet in diameter ? Ans. ^(452)

Page 133 - AB may be comFIG. 74. puted (How?). 93. V. To find the Distance of an Inaccessible Object. Let A (Fig. 75) be the position of the observer and let it be required to determine the distance from A to B. Let the pupil determine what measurements and computations are necessary in accordance with the figure. FIG. 75. 94. VI. To find the Distance between two Objects separated by an Impassable Barrier (and possibly invisible to each other).

Page 108 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.

Page 186 - THEOREM. Every section of a sphere, made by a plane, is a circle.