Elements of Plane and Spherical Trigonometry: With Practical Applications |
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Page 62
... observe that the wall of a fort upon the opposite brink subtends an angle at the point of observation of 36 ° 52 ′ 12 ′′ ; required the height of the wall . Ans . 30 feet . 2. The angle of elevation of the top of a flag - staff ...
... observe that the wall of a fort upon the opposite brink subtends an angle at the point of observation of 36 ° 52 ′ 12 ′′ ; required the height of the wall . Ans . 30 feet . 2. The angle of elevation of the top of a flag - staff ...
Page 63
... observe the horizontal an- gles CA B and CBA . Then , in A B the triangle AB C , there will be known the side AB and the angles ; therefore the sides AC and BC can be found by Art . 125 . EXAMPLES . 1. Wanting to know the distances of ...
... observe the horizontal an- gles CA B and CBA . Then , in A B the triangle AB C , there will be known the side AB and the angles ; therefore the sides AC and BC can be found by Art . 125 . EXAMPLES . 1. Wanting to know the distances of ...
Page 64
... observed an eagle's nest on an inaccessible mountain - crag on the opposite side , and being de- sirous of ascertaining its height above the level of the river , he measured along the shore a straight line 110 yards in length , and ...
... observed an eagle's nest on an inaccessible mountain - crag on the opposite side , and being de- sirous of ascertaining its height above the level of the river , he measured along the shore a straight line 110 yards in length , and ...
Page 65
... from which both the objects are visible . Measure the base line A B , and observe the angles DA B , D B A , CA B , and CBA . Then , in the Required the distance A B triangle DAB , since we have the side A B. BOOK IV . 65.
... from which both the objects are visible . Measure the base line A B , and observe the angles DA B , D B A , CA B , and CBA . Then , in the Required the distance A B triangle DAB , since we have the side A B. BOOK IV . 65.
Page 66
... Observe the angles ADC and BDC . Describe a circle about the tri- angle A DB , and draw A E and EB ; then the angle A B E is equal to the angle A D E , since both are measured by half of the same arc A E ( Geom . , Prop . XVIII . Bk ...
... Observe the angles ADC and BDC . Describe a circle about the tri- angle A DB , and draw A E and EB ; then the angle A B E is equal to the angle A D E , since both are measured by half of the same arc A E ( Geom . , Prop . XVIII . Bk ...
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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.