## Elements of Plane and Spherical Trigonometry: With Practical ApplicationsR.S. Davis & Company, 1867 - 170 pages |

### From inside the book

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Page 38

With Practical Applications Benjamin Greenleaf. 102. If the

With Practical Applications Benjamin Greenleaf. 102. If the

**angle**or arc is between ...**angle**or arc is expressed in degrees , minutes , and seconds , find the ...**included**in the table , since they may be readily derived from the cosines ... Page 43

...

...

**included angle**. Let ABC be any plane triangle , in which the sides opposite the angles A , B , C , respectively , are denoted by a , b , c . Draw BD from one of the angles , B , perpendicular to the opposite side , AC . Then , if A is ... Page 53

... angles . 3. Given the perpendicular of a right - angled triangle equal to 2.269 rods , and the base equal to 126.9 rods ...

... angles . 3. Given the perpendicular of a right - angled triangle equal to 2.269 rods , and the base equal to 126.9 rods ...

**included angle**. IV . The three sides . CASE I. 125. Given one side and two angles . Let there be given in the ... Page 57

... angles . Ans . Impossible . CASE III . 128. Given two sides and the

... angles . Ans . Impossible . CASE III . 128. Given two sides and the

**included angle**. Let there be given in the triangle ABC the sides a and b and the**included angle**C , to solve the triangle . To find A and B , we have A + B = 180 ° C ... Page 58

... angle . Since have That is , ( A + B ) is known , when ( AB ) is found , we ≥ A = ↓ ( A + B ) + § ( A — B ) , B ...

... angle . Since have That is , ( A + B ) is known , when ( AB ) is found , we ≥ A = ↓ ( A + B ) + § ( A — B ) , B ...

**included angle**C equal to 55 ° 30 ′ 26 ′′ ; to find the side c and the angles A and B. Solution . A + B = 180 ° C = 124 ...### Other editions - View all

### Common terms and phrases

A+ log acute angle adjacent sides angle equal angle of elevation angle opposite angle or arc ar.co.log arithm arithmetical complement column headed cos a cos cos a sin cos² cosec Cotang coversed sine decimal denoted divided equal to 90 equation feet find the SINE formulę Geom given number Given the hypothenuse half the sum half their difference Hence included angle log blog log cos log cot log sin logarithmic cosine logarithmic sine logarithmic tangent M.
M. Sine minus the logarithmic Napier's rules negative oblique oblique-angled spherical triangle perpendicular plane triangle Prop right-angled spherical triangle right-angled triangle equal rods secant side A C side b equal side opposite sin A cos sin a sin sin² sine and cosine Solution solve the triangle spherical triangle ABC SPHERICAL TRIGONOMETRY subtract sun's declination suvers Tang tangent of half three sides trigonometric functions values whence yards

### Popular passages

Page 75 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...

Page 33 - 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.

Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 4 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art.

Page 3 - FRACTION is a negative number, and is one more than the number of ciphers between the decimal point and the first significant figure.

Page 43 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.

Page 85 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. II. The sine of the middle part is equal to the product of the cosines of the opposite parts.

Page 46 - ... sides, into half the sum less the side opposite the angle, divided by the rectangle of the two adjacent sides, 117. Dividing (102) by (106), (103) by (107), and (104) by (108), we have, by (13...

Page 71 - From a window near the bottom of a house, which seemed to be on a level with the bottom of a steeple, I took the angle of elevation of the top of the steeple, equal to 40° ; then from another window, 18 feet directly above the former, the like angle was 37° 30'.

Page 11 - ... multiplied by it will give a negative result ; but that which is to be carried from the decimal part will be positive; therefore, their difference will be the characteristic of the product. Ex. 1. Required the square, or second power, of 31. Log 31 = 1.491362 2 Ans. 961 2.982724 2. Required...