...on it let fall a perpendicular from the opposite angle. Then, as the base is to the sum of the other sides, so is the difference of those sides to the difference of the segments of the base. Half this difference added to half the base will give the greater segment, and subtracted will give...

...given straight line. 184. Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex : construct the triangle. 185. Given the vertical angle, and the lengths of two lines...

...given straight line. 130. Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle. 131. Given the vertical angle, and the lengths of two lines...

...method, though little used, will find an angle, when three sides are given. As the base, or longest side, is to the sum of the other two sides, so is the difference...the segments of the base, made by a perpendicular drawn from the opposite angle. Then the half difference added to half the base, gives the segment adjacent...

...the sum of the sides. PROBLEM II. — In a plane triangle are given the ratio of the two sides, and the segments of the base made by a perpendicular let fall from the opposite angle on the base, to determine the triangle. . the ratio of BC to AC as m ,.. I to n, and...

...8 1 in. Ans. Again: 251^ @ 2s. 6d = 7546^. = £& 8í. 10|</. Ans. 2. If AB = 28, BC = 45, CA = 53, the difference of the segments of the base made by a perpendicular from A on BC = (CA + AB)(CA-AB)-7-BC = 81 x 254-45 = 45 = BC ; Л ABC is a right angle, and the area...

...base is a circle. 31. Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex, to construct the triangle. 32. Show that the locus of the middle point of a straight...

...given straight line. 130. Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle. 131. Given the vertical angle, and the lengths of two lines...

...angle to the opposite side, and the perpendicular given, to construct the triangle. 124. Two sides and the difference of the segments of the base made by a perpendicular from the vertical angle to the base given, to construct the triangle. Is there any ambiguity in this...

...produced: EA C is the A. Ex. 46. Given the vertical angle, the difference of the sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex: construct the triangle. Take AB = difference of base segments; make £ABC — | given...