height is unknown, but the diagonal (a right line drawn from corner to corner) is found by measurement to be 15 inches, 32 hundredths. What is the height ?
Note. A diagonal cuts the oblong square or rect- angle into two rectangular triangles, of which the height above required is one of the smaller sides.
8,54 15,32 As a smaller side is re-
8,54 15,32 quired, subtract the known
smaller from the larger.
3416 3064
4270 4596 234,7024
6832 7660 72,9316
1532 --
72,9316 ----161,7708
234,7024
It remains to find a number, which multiplied by it- self will give 161,770. A few trials will show that this is (as near as possible) 12,719 as may be found by multiplying this number by itself. The height then, is 12 inches, and 719 thousandths of an inch.
Example 3. Find the height of an isoceles triangle, (1st Class, Prob. 27.) whose base is 52 and the equal sides, 87. The perpendicular, drawn from the summit, cuts the base in halves, and is one side of a rectan- gular triangle, of which
the base i§ half the larger one, or . . 26 The great side of the new angle, which 26
was one of the equal sides of the -
isoceles, is........ 87 156
87 52
From 7569 - -
Take 676 609 676
--696
6893 • -
7569
