 | Miles Bland - 1830 - 394 pągines
...area of the triangle ; determine the remaining sides and angles. 54. Having given the lengths of three lines drawn from the angles of a triangle, perpendicular to the opposite sides ; determine the sides and angles. 55. Having given the three angles of a triangle, and the radius of... | |
 | University of Sydney - 1853 - 810 pągines
...the expansion of Find the term not involving x in the expansion of 1 ' B. 5. Show that the straight lines drawn from the angles of a triangle perpendicular to the opposite sides meet in a point. 6. Describe an isosceles triangle having each of the angles at the base double the third angle. Hence... | |
 | Isaac Todhunter - 1855 - 332 pągines
...(2x - a) (x' - 2o) ; .-. 3ax = a (x' + a) ; Substitute this value of x in (2) and we find y = y'. 9 3 We have thus determined the co-ordinates of the point...line through A perpendicular to BC is, (Art. 44), The equation to AC is r hence the equation to the line through B perpendicular to AC is (5)The line... | |
 | Isaac Todhunter - 1855 - 376 pągines
...(2ic — a) (x — 2a) ; .'. 3ax = a(x +a) ; Substitute this value of x in (2) and we find y' y=BWe have thus determined the co-ordinates of the point...line through A perpendicular to BC is, (Art. 44), y The equation to AC is ... (4). hence the equation to the line through B perpendicular to AC is The... | |
 | Richard Dunkley Beasley - 1858 - 144 pągines
...in D so that AD :BD=CB: CA. Shew that 96. If tan"1 x + I sec"1 5x = 45°, then x=±\, Ą О 97. If the lines drawn from the angles of a triangle perpendicular to the opposite sides meet in a point whose distances from the three angles are p, q, r, respectively, then the area of the triangle is -(pa... | |
 | John Hymers - 1858 - 324 pągines
...is fulfilled, are exactly the same as for plane triangles, as we shall now shew. 17. The three arcs drawn from the angles of a triangle perpendicular to the opposite sides, or bisecting the angles or opposite sides, or meeting the opposite sides in the points where they are... | |
 | Isaac Todhunter - 1859 - 156 pągines
...cos B , cos C cos.Z?'cosC" cos ^4 cos (7' cos .4 cos 5' 8. If p, q, r be the arcs of great circles drawn from the angles of a triangle perpendicular to the opposite sides, (a, a'), (ft, {?), (y, y') the segments into which these arcs are divided, shew that tan a tan a' =... | |
 | Isaac Todhunter - 1862 - 376 pągines
...line represented by (1) passes through the intersection of the lines represented by (2) and (3), whic. proves the proposition. The lines drawn from the angles of a triangle perpendicula' to the opposite sides meet in a point. The equation to BC is (Art.. 35) hence the equation... | |
 | Isaac Todhunter - 1863 - 182 pągines
...ta.nOF are respectively equal to cos A cos B . cos C . * 8. If p, q, r be the arcs of great circles drawn from the angles of a triangle perpendicular to the opposite sides, (a, a), (/?, /?), (y, y') the segments into which these arcs are divided, shew that tan a tan a' =... | |
 | John Hunter (of Uxbridge.) - 1866 - 104 pągines
...=2*;, and the difference of the angles at the base is 30°. Find the locus of the vertex. 12. Shew that the lines drawn from the angles of a triangle perpendicular to the opposite sides meet at a point ; and that the locus of that point, for all equal triangles on the same base, is a parabola... | |
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... proves the proposition. The lines drawn from the angles of a triangle perpendicular to the opposite sides meet in a point. The equation to BC is, (Art. 35), hence the equation to the line through A perpendicular to BC is, (Art. 44), y The equation... 
