A 7 m long flagstaff is fixed on the top of a tower. From a point on the ground, the angles of elevation of the top and bottom of the flagstaff are 450 and 360 respectively. Find the height of the tower correct to one place of decimal
Solution:
Consider TR as the tower and PT as the flag on it
PT = 7 m
Take TR = h and AR = x
Angles of elevation from P and T are 450 and 360
In right triangle PAR
tan θ = PR/AR
Substituting the values
tan 450 = (7 + h)/ x
So we get
1 = (7 + h)/ x
x = 7 + h …. (1)
In right triangle TAR
tan θ = TR/AR
Substituting the values
tan 360 = h/x
So we get
0.7265 = h/x
h = x (0.7265) …… (2)
Using both the equations
h = (7 + h) (0.7265)
By further calculation
h = 7 × 0.7265 + 0.7265h
h – 0.7265h = 7 × 0.7265
So we get
0.2735h = 7 × 0.7265
By division
h = (7 × 0.7265)/ 0.2735
We can write it as
h = (7 × 7265)/ 2735
h = 18.59 = 18.6 m
Hence, the height of the tower is 18.6 m.