## Elements of Plane and Spherical Trigonometry: With Practical Applications |

### From inside the book

Results 1-5 of 18

Page 48

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**feet**and A = 59 ° 37′42 ′′ , and we have , by ( 112 ) and ( 113 ) , h = 1785.395 log 3.251734 A 59 ° 37 ' 42 " log ...**feet**; base , 902.708**feet**. 2. Given the hypothenuse of a right - angled triangle equal to 25 yards , and one of the ... Page 50

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**feet**, and the acute angle A equal to 59 ° 37 ′ 42 " ; to solve the triangle . Solution . The angle B 90 ° By ( 114 ) ...**feet**; hy- pothenuse , 1785.395**feet**. 2. Given one of the sides about the right angle of a right- angled triangle ... Page 51

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**feet**; angle at the base , 59 ° 37 ′ 42 ′′ ; angle at the perpendicular , 30 ° 22 ′ 18 ′′ . 2. Given the hypothenuse of a right - angled triangle equal to 73**feet**, and one of the sides equal to 55**feet**; to solve the triangle . 3 ... Page 52

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**feet**, and the side b equal to 902.708**feet**; to solve the triangle . Solution . By ( 122 ) and ( 124 ) , we have 1540.37 log 3.187626 = 902.708 ar . co . log 7.044453 p b d A 59 ° 37 ′ 42 ′′ log tan - log 3.187626 ar . co . log sin A ... Page 53

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**feet**, and the base equal to 72**feet**; to find the hypothenuse and the two acute angles . 3. Given the perpendicular of a right - angled triangle equal to 2.269 rods , and the base equal to 126.9 rods ; required the hy- pothenuse and ...### Other editions - View all

### 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.