Plane trigonometry, by S.L. Loney.

HEIGHTS AND DISTANCES.

43

DB 200
200- x — -
200
so that x =200 - = 1331 feet.
3
Ex. 4. A man observes that at a point due south of a certain tower its
angle of elevation is 60~; he then walks 300 feet due west on a horizontal
plane and finds that the angle of elevation is then 30~; find the height of
the tower and his original distance from it.,A,,, 1M x
x
A M
p 300
B X,3 M AJL M
13
Let P be the top, and PM11 the height, of the tower, A the point due
south of the tower and B the point due west of A.
The angles PMA, PMB, and MAB are therefore all right angles.
For simplicity, since the triangles PAM, PBM, and ABM are in
different planes, they are reproduced in the second, third, and fourth
figures and drawn to scale.
We are given A B 300 feet, L PAM=60~, and L PBM= 30~.
Let the height of the tower be x feet.
From the second figure
AM / 1
- = cot 60~=,
x d3
so that AM1= x
From the third figure
B = cot 300 =,/3,
so that BM= /3.,x
so that BM1= 3.x,