Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics, and Hydrostatics. With Tables ... and ReferencesLongmans, Green & Company, 1877 - 413 σελίδες |
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Σελίδα 75
... tower at a distance of 20 yards from its foot is three times as great as the angle of elevation 100 yards from the same point . Show that the height of the tower in feet is 300 XLVII . 1. Produce a given straight line so that the ...
... tower at a distance of 20 yards from its foot is three times as great as the angle of elevation 100 yards from the same point . Show that the height of the tower in feet is 300 XLVII . 1. Produce a given straight line so that the ...
Σελίδα 95
... tower 400 ft . high , when due north of an observer was 55 ° 14 ' ; what will be the angle of elevation to the observer when he has walked to a point 720 ft . due west of his former position ? LVIII . 1. In 1370695 oz . how many tons ...
... tower 400 ft . high , when due north of an observer was 55 ° 14 ' ; what will be the angle of elevation to the observer when he has walked to a point 720 ft . due west of his former position ? LVIII . 1. In 1370695 oz . how many tons ...
Σελίδα 127
... tower standing on the plane . The angles of elevation of the tower from the two ends of the measured line are 30 ° and 18 ° respectively . Find the height of the tower . 9. Prove that 2 cos 0 = e 07-1 -07-1 + ε > √1 -97-1 21 sin 0ɛ -ε ...
... tower standing on the plane . The angles of elevation of the tower from the two ends of the measured line are 30 ° and 18 ° respectively . Find the height of the tower . 9. Prove that 2 cos 0 = e 07-1 -07-1 + ε > √1 -97-1 21 sin 0ɛ -ε ...
Σελίδα 133
... tower which stands on a horizontal plane is 200 feet high , and there is a small loophole in the tower at a certain height above the ground ; an observer is at a horizontal distance from the tower of 300 feet , but stands on a mound so ...
... tower which stands on a horizontal plane is 200 feet high , and there is a small loophole in the tower at a certain height above the ground ; an observer is at a horizontal distance from the tower of 300 feet , but stands on a mound so ...
Σελίδα 166
... sin C 1 ( 1 ) a = b = ; с 2R sin B + sin C - sin A B ( 2 ) = tan tan sin B + sin C + sin A 2 2 A C ( 3 ) ( b − c ) cot — + ( c − a ) cot 3+ ( a − b ) cot = 0 . 8. A tower seventy feet high stands on the top 166 WOOLWICH.
... sin C 1 ( 1 ) a = b = ; с 2R sin B + sin C - sin A B ( 2 ) = tan tan sin B + sin C + sin A 2 2 A C ( 3 ) ( b − c ) cot — + ( c − a ) cot 3+ ( a − b ) cot = 0 . 8. A tower seventy feet high stands on the top 166 WOOLWICH.
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
Arithmetic axis ball base bisected body cent centre of gravity circle coefficient of friction compound interest cone cost crown 8vo cube cubic foot curve Define determine diameter Divide dwts ellipse English equal equilibrium expression feet Find the area Find the centre Find the distance Find the equation Find the number Find the sum Find the value fluid forces acting fraction geometrical Grammar horizontal plane hyperbola inches inclined plane inscribed Integrate isosceles latus rectum least common multiple length logarithms miles Multiply parabola parallel particle perpendicular pressure Prove pulleys radius ratio rectangle rectangular Reduce right angles sides simple interest sin² sine spherical triangle square root straight line string subtended Subtract surface tangent theorem tons tower triangle ABC velocity vertical vulgar fraction weight yards
Δημοφιλή αποσπάσματα
Σελίδα 123 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 10 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Σελίδα 184 - If two straight lines cut one another within a circle, the rectangle contained by the segments of one of them, is equal to the rectangle contained by the segments of the other.
Σελίδα 78 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 184 - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third (20.
Σελίδα 184 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Σελίδα 163 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 184 - In right angled triangles the square on the side subtending the right angle is equal to the (sum of the) squares on the sides containing the right angle.
Σελίδα 154 - If two straight lines be cut by parallel planes, they shall be cut in the same ratio. Let the straight lines AB, CD be cut by the parallel planes GH, KL, MN, in the points A, E, B; C, F, D : As AE is to EB, so is CF to FD.