Elements of Plane and Spherical Trigonometry: With Practical Applications |
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Page 60
... 95.12 , 162.34 , and 98 ; to solve the triangle by means of the tangent . Ans . The angles , 32 ° 14 ′ 53 ′′ ; 114 ° 24 ′ 9 ′′ ; 33 ° 20 ′ 58 ′′ . BOOK IV . PRACTICAL APPLICATIONS . DETERMINATION OF HEIGHTS AND 60 TRIGONOMETRY.
... 95.12 , 162.34 , and 98 ; to solve the triangle by means of the tangent . Ans . The angles , 32 ° 14 ′ 53 ′′ ; 114 ° 24 ′ 9 ′′ ; 33 ° 20 ′ 58 ′′ . BOOK IV . PRACTICAL APPLICATIONS . DETERMINATION OF HEIGHTS AND 60 TRIGONOMETRY.
Page 61
With Practical Applications Benjamin Greenleaf. BOOK IV . PRACTICAL APPLICATIONS . DETERMINATION OF HEIGHTS AND DISTANCES . 131. A HORIZONTAL ... height BC . • Measure from the foot of the object , in the 6 * BOOK IV PRACTICAL APPLICATIONS.
With Practical Applications Benjamin Greenleaf. BOOK IV . PRACTICAL APPLICATIONS . DETERMINATION OF HEIGHTS AND DISTANCES . 131. A HORIZONTAL ... height BC . • Measure from the foot of the object , in the 6 * BOOK IV PRACTICAL APPLICATIONS.
Page 62
... height of the wall . Ans . 30 feet . 2. The angle of elevation of the top of a flag - staff , measured on a horizontal plane , at a distance of 89 feet from the foot of the staff , is 41 ° 29 ' ; what is the height of the staff ? 134 ...
... height of the wall . Ans . 30 feet . 2. The angle of elevation of the top of a flag - staff , measured on a horizontal plane , at a distance of 89 feet from the foot of the staff , is 41 ° 29 ' ; what is the height of the staff ? 134 ...
Page 63
... height of an inaccessible object above a hori- zontal plane . First Method . Let B be the top of the object , and let it be required to find the height B C. Measure a horizontal base line , A C ' , of any convenient length , directly ...
... height of an inaccessible object above a hori- zontal plane . First Method . Let B be the top of the object , and let it be required to find the height B C. Measure a horizontal base line , A C ' , of any convenient length , directly ...
Page 64
... height BC by Art . 120 . EXAMPLES . 1. Required the altitude of a hill whose angle of elevation , taken at the foot of it , was 55 ° 54 ' , and 300 feet back , on the same horizontal plane with the foot , the angle was 33 ° 20 ′ . Ans ...
... height BC by Art . 120 . EXAMPLES . 1. Required the altitude of a hill whose angle of elevation , taken at the foot of it , was 55 ° 54 ' , and 300 feet back , on the same horizontal plane with the foot , the angle was 33 ° 20 ′ . Ans ...
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Common terms and phrases
A B C A+ log acute angle adjacent sides Algebra angle equal angle of elevation angle opposite angle or arc ar.co.log Arithme column headed cos² cosec Cotang decimal denoted divided Elementary Algebra equation Equations Art EXAMPLES feet find the SINE formulæ Geom Geometry given number Given the hypothenuse Greenleaf's New Series half the sum Hence included angle 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 Parker's Exercises perpendicular plane triangle Prop right-angled spherical triangle right-angled triangle equal rods School secant side b equal side opposite sin A cos sin A sin sin a+b sin² sine and cosine Solution solve the triangle spherical triangle ABC SPHERICAL TRIGONOMETRY subtract sun's declination suvers suversed sine Tang tangent of half trigonometric functions values whence yards
Popular passages
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 7 - This process, like its converse (Art. 23), is based upon the supposition that the differences of logarithms are proportional to the differences of their corresponding numbers.
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. 9) M=a*, then, raising both sides to the wth power, we have Mm = (a")m = a"" . Therefore, log (M m) = xm = (log M) X »»12.
Page 74 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b...
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 39 - ... be at the head of the column, take the degrees at the top of the table, and the minutes on the left ; but if the name be at the foot of the column, take the degrees at the bottom, and the minutes on the right.
Page 46 - The cosine of half of any angle of a plane triangle is equal to the square root of half the sum of the three sides, into half the sum less the side opposite the angle, divided by the rectangle of the two adjacent sides.