Military examinations. Mathematical examination papers set at an open competition for admission to the Royal military college, Sandhurst, and for first appointments in the Royal marine light infantry, held under the directions of the Civil service commissioners, 1883, with solutions by J.F. and T. Heather
48 feet angular point assumed ay)³ base by)³ called centre circle circular measure circumference cos² cuts describe diameter diff difference digits distance divided double draw equal equation equivalent EXAMINATION expressed feet long figure Find four right angles fraction given gives Greatest Common Measure Hence hour least number length less let fall logarithm manner MARINE LIGHT INFANTRY MATHEMATICAL mean proportional metal miles minutes parallelogram perpendicular produced Prove quantities radius raised ratio rectangle contained represent ridge roof root ROYAL MARINE LIGHT ROYAL MILITARY COLLEGE Show sides silver sin² sine slope SOLUTIONS square straight line tan² tangent triangle A B C unit walks walls weight whence whole worth ОР دو وو
Page 12 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Page 14 - In equal circles, angles, whether at the centres or circumferences, have the same ratio which the circumferences on which they stand have to one another ; so also have the sectors.
Page 13 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle.
Page 15 - In the ordinary or sexagesimal system, a right-angle, which is used as the measure of all plane angles, is divided into 90 equal parts, called degrees; a degree is divided into 60 equal parts, called minutes ; and a minute into 60 equal parts, called seconds.
Page 18 - Ans. ty. 7. Prove that the sides of any plane triangle are proportional to the sines of the angles opposite to these sides. If 2s = the sum of the three sides (a, b, c) of a triangle, and if A be the angle opposite to the side a, prove that sin A = ^ Vs (s -a)(s — b) (s — c).
Page 14 - ... being 10 in. ; (2) 1.5 radians, radius 2 ft. ; (3) 4.3 radians, radius 21 yd. ; (4) 1.25 radians, radius 8 in. 4. The value of the division on the outer rim of a graduated circle is 5', and the distance between the two successive divisions is .1 of an inch. Find the radius of the circle. 5. Show that the distance in miles between two places on the equator, which differ in longitude by 3° 9', assuming the earth's equatorial diameter to be 7925.6 mi., is 217.954 mi. 6. (a) The difference of two...
Page 13 - TRIANGLES. 33. Given the vertical angle, one of the sides containing it, and the length of the perpendicular from the vertex on the base : construct the triangle. 34. Given the feet of the perpendiculars drawn from the vertices on the opposite sides : construct the triangle. 35. Given the base, the altitude, and the radius of the circumscribed circle : construct the triangle. 36. Given the base, the vertical...
Page 12 - IF a straight line be divided into two equal parts, and also into two unequal parts : the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.