Oil A 1'. VIII.

GEOMETRY.

SKI

tower, the distance, K II, being Id yards ; the angle taken at K, 20° being first set out,it will then easily be perceived that the height may be ascertained by the scale.

The height of the observatory O P from the station at It, may also be accurately ascer-tained by constructing the angle YTV, and setting off the distance TX, and thenmeasuring by the scale theheight Xa. The angleZ X T is here a right angle,and the distance from Tto X is 17 yards.

Inaccessible heights maybe measured by having twostations, as C and D : afterthe distance between themis ascertained, take theangles II C D from the sta-tion 0, and the angle IIDC

Fig. 975.

I'ig. 977.

Fig.978.

from the station D : then construct the angle L G O, and the angle G I VI, and by meansof the scale the height ON may be measured, which will correspond to the height A B.

The height from P to It may be ascertained in a similar way: from the point S,measure the angleTSR, and from thepoint T the angleS TII, also the dis-tance between the sta-tions S, T: then con-struct a scale Q, drawthe line V K, and setoff the measurementof the distance takenbetween S and T,which is VX: at V

and X set out the 1 980 ‘

angles taken at the tw*o respective stations; the height Z Y will be that of P R.

The height of the tower All, which is inaccessible, may also be found by means^ ^ after the observations have been made, draw the line

of the demicirele placed at D C :

Fig. 981.

Fig. 982.

GH by the scale: from the point G draw the angle GKL equal to the angle CD A, andthe angle I N VI equal to DAB : the dimension or length of line P O by the scale willbe the height of the tower A 11.

The height from one portion of a building to another may also he readily found, as thedifference between the levels at Rand S: place the piquets at V and T, and measure thefour angles '1 VR , TVS, VTS, VTK, and also the distance between V and T.