## Plane and Spherical Trigonometry |

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acute altitude angle angle of elevation answer antilog base called chord circle circular colog computed construct cos x cosine cotangent Cotg decimal denoted determine diagonal difference divided earth equal equation example Exercise Express figure Find the area Find the distance Find the value five-place formula four four-place tables geometry given gives greater height Hence horizontal included isosceles known latitude length less Let the pupil log cot logarithms manner mantissa measured method miles minutes negative oblique observer obtained opposite perpendicular places plane positive Prove quadrant radians radius ratio regular respectively right triangle rule side Similarly sin x sine sinš solution solve square Subtract taken Tang tangent third tower trigonometric functions unknown vertex

### 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.