Question

From an observation tower that overlooks a runway, the angles of depressin of point A, on one side of the runway, and point B, on the opposite side of the runway are, 6degree and 13degree, respectively. The points and the tower are in the same vertical plance and the distance from A and B is 1.1km. Determine the height of the tower.

Answer 1

Draw 2 rt triangles witha common ver. side.
h = Y = Ver. side.
1.1km+X = Hor. side.
X = dist. from hyp. of smaller triangle to base of tower.

tan6 = h/(1.1+X).
h = (1.1+X)tan6.

tan13 = h/X
h = X*tan13.

h = (1.1+X)tan6 = X*tan13
(1.1+X)tan6 = X*tan13
1.1*tan6+X*tan6 = X*tan13
X*tan6-X*tan13 = -1.1*tan6
0.1051x-0.2309x = -0.1156
-0.12577x = -0.1156
X = 0.92 km.

h = X*tan13 = 0.212 km. = 212 m.