Mathematical Exercises ...1867 |
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Page 116
... vertical line ; an observer takes up a position in the horizontal plane at a distance of 350 yards from the point where the balloon left the earth ; after a time he observes the angle of elevation of the balloon to be 55 ° 17 ' , and ...
... vertical line ; an observer takes up a position in the horizontal plane at a distance of 350 yards from the point where the balloon left the earth ; after a time he observes the angle of elevation of the balloon to be 55 ° 17 ' , and ...
Page 123
... vertical column , stand- ing on the same horizontal plane , were observed 22 ° 15 ′ and 44 ° 30 ' : find the height of the column . 9. A lighthouse was observed from a ship to bear N. 45 ° E .; and after the ship had sailed 4 miles SE ...
... vertical column , stand- ing on the same horizontal plane , were observed 22 ° 15 ′ and 44 ° 30 ' : find the height of the column . 9. A lighthouse was observed from a ship to bear N. 45 ° E .; and after the ship had sailed 4 miles SE ...
Page 135
... vertical angle is a right angle , and radius of base 10 feet , is bisected by a plane parallel to the base . Find the radius of the section . XCVII . 1. Reduce to their simplest forms : - ( 1 ) 3+ } + { −11 ; ( 2 ) ( 63 + 2 } ) ; - ( 3 ) ...
... vertical angle is a right angle , and radius of base 10 feet , is bisected by a plane parallel to the base . Find the radius of the section . XCVII . 1. Reduce to their simplest forms : - ( 1 ) 3+ } + { −11 ; ( 2 ) ( 63 + 2 } ) ; - ( 3 ) ...
Page 150
... 315 ° and 360 ° ; and find the sine of 9 ° . 11. If any number of triangles on the same base B C and on the same side of it have their vertical angles equal , and perpendiculars meeting in D be drawn from B , C 150 WOOLWICH.
... 315 ° and 360 ° ; and find the sine of 9 ° . 11. If any number of triangles on the same base B C and on the same side of it have their vertical angles equal , and perpendiculars meeting in D be drawn from B , C 150 WOOLWICH.
Page 152
... vertical straight line observes the angles of elevation of its ends to be 49 ° 27 ' and 38 ° 51 ' . Find its length . 12. The angles of a plane triangle form a geometrical progression of which the ratio is 2. Show that the greatest side ...
... vertical straight line observes the angles of elevation of its ends to be 49 ° 27 ' and 38 ° 51 ' . Find its length . 12. The angles of a plane triangle form a geometrical progression of which the ratio is 2. Show that the greatest side ...
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Common terms and phrases
acting amount angle axis base body CALC cent centre of gravity circle coefficient common contained cost cubic curve decimal described determine diameter difference direction distance Divide drawn elevation ellipse equal equilibrium Explain Express Extract the square feet Find the number Find the value fluid force fraction give given greatest horizontal plane hour inches inclined plane interest length logarithms lowest means measure miles moving Multiply observed parallel passing perpendicular places plane position pressure projected Prove radius Reduce remaining respectively rest result right angle sides simple Solve the equations square square root straight line string surface tables tangent tons train triangle TRIG velocity vertical volume weight whole yards
Popular passages
Page 12 - 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 109 - From the top of a hill the angles of depression of two successive milestones, on a straight level road leading to the hill, are observed to be 5° and 15°.
Page 279 - Find the distance of the centre of gravity of the remainder from the intersection of the diagonals.
Page 374 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 221 - A body is projected with a velocity v in a direction making an angle a with the horizon...
Page 225 - Hence the conditions of equilibrium of any system of forces, acting in one plane upon a rigid body, may be obtained as follows ; I.
Page 198 - A manufacturer having a capital of £5000 on which he can realise by hand labour 10 per cent. profit, buys a machine for £1000, by which his profit on the remainder of his capital is raised to 20 per cent. This machine lasts 5 years. Of how...
Page 84 - A number is divisible by 9 if the sum of its digits is divisible by 9.
Page 291 - Assuming the parallelogram of forces, prove that the algebraic sum of the moments of two forces about a point in the space between their directions is the same as the moment of their resultant.
Page 165 - One company guarantees to pay 5 per cent. on shares of £100 each; another guarantees at the rate of 4f per cent.