A Treatise on Plane and Spherical Trigonometry: And Its Applications to Astronomy and Geodesy with Numerous ExamplesD.C. Heath & Company, 1892 - 368 páginas |
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Página 183
... tower , which subtends an angle of 22 ° 30 ' at the edge of the remote bank ; find the height of the tower . Ans . 124.26 feet . 2. At 360 feet from the foot of a steeple the elevation is half what it is at 135 feet ; find its height ...
... tower , which subtends an angle of 22 ° 30 ' at the edge of the remote bank ; find the height of the tower . Ans . 124.26 feet . 2. At 360 feet from the foot of a steeple the elevation is half what it is at 135 feet ; find its height ...
Página 196
... tower , the angle of elevation of the top of the tower is observed to be 60 ° : find the height of the tower . Ans . 346 feet . 93. From the top of a vertical cliff , the angle of depres- sion of a point on the shore 150 feet from the ...
... tower , the angle of elevation of the top of the tower is observed to be 60 ° : find the height of the tower . Ans . 346 feet . 93. From the top of a vertical cliff , the angle of depres- sion of a point on the shore 150 feet from the ...
Página 197
... tower are observed to be 75 ° and 60 ° respectively : find the height of the cliff . Ans . 86.6 feet . 99. A man walking a straight road observes at one mile- stone a house in a direction making an angle of 30 ° with the road , and at ...
... tower are observed to be 75 ° and 60 ° respectively : find the height of the cliff . Ans . 86.6 feet . 99. A man walking a straight road observes at one mile- stone a house in a direction making an angle of 30 ° with the road , and at ...
Página 199
... tower is situated on the top of a hill whose angle of inclination to the horizon is 30 ° . The angle subtended by the tower at the foot of the hill is found by an observer to be 15 ° ; and on ascending 485 feet up the hill the tower is ...
... tower is situated on the top of a hill whose angle of inclination to the horizon is 30 ° . The angle subtended by the tower at the foot of the hill is found by an observer to be 15 ° ; and on ascending 485 feet up the hill the tower is ...
Página 200
... tower 51 feet high has a mark 25 feet from the ground : find at what distance the two parts subtend equal angles to an eye 5 feet from the ground . Ans . 160 feet . ६ 125. From the extremities of a sea - wall , 300 feet long , the ...
... tower 51 feet high has a mark 25 feet from the ground : find at what distance the two parts subtend equal angles to an eye 5 feet from the ground . Ans . 160 feet . ६ 125. From the extremities of a sea - wall , 300 feet long , the ...
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Otras ediciones - Ver todas
A Treatise on Plane and Spherical Trigonometry: And Its Applications to ... Edward Albert Bowser Sin vista previa disponible - 2013 |
Términos y frases comunes
algebraically angle AOP angle of elevation base calculate centre circle circular measure common logarithms cos b cos cos² cosec cotangent decimal places denote diff equal equations EXAMPLES expression feet find log find the angle find the height find the number formulæ Given log Hence horizon hypotenuse integer log cot log sin log sine mantissa Multiply negative number whose logarithm observed obtained opposite perpendicular plane polar triangle positive Prove the following quadrant R₁ r₂ radian radius right angles right triangle sec² secant sides Similarly sin a cos sin B sin sin x sin² sin³ sines and cosines sinx siny solution Solve spherical triangle subtends table of logarithms table of natural tan² tangent triangle ABC trigonometric functions vertical yards ОР
Pasajes populares
Página 148 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.
Página 147 - Law of Sines. — In any triangle the sides are proportional to the sines of the opposite angles.
Página 278 - AB'C, we have by (4) cos a' — cos b cos c' + sin b sin c' cos B'AC, or cos(тг— a) = cos b cos(тг— c) + sin b sin(тт — C)COS(тг —A). .-. cos a = cos b cos с + sin b sin с cos A.
Página 278 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.
Página 278 - 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...
Página 6 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Página 17 - If the cosine of A be subtracted from unity, the remainder is called the versed sine of A. If the sine of A be...
Página 89 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 149 - 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.