Question

A 7m long flagstaff is fixed on top of a tower on the horizontal plane. from a point on the ground, the angle of elevation of the top and bottom of the flafstaff are 45degrees and 60degrees respectively. find the height of the tower

Answer 1

Answer:

16.56 m

Explanation:

Let's consider that the height of tower is h and distance of that point from the foot of tower is d.

As given in question,

• height of flag = 7 m
• angle of elevation of top of the flag = 45°
• angle of elevation of bottom of the flag = 60°

Now, according to question,

$tan60^o\ =\ \dfrac{h}{d}$

$=>\ d\ =\ \dfrac{h}{tan60^o}$

$=>\ d\ =\ \dfrac{h}{\sqrt{3}}$         (1)

$tan45^o\ =\ \dfrac{h-7}{d}$

$=>\ d\=\ \dfrac{h-7}{tan45^o}$

$=>\ d\ =\ h-7$                 (2)

from equation (1) and (2), we have

$h-7\ =\ \dfrac{h}{\sqrt{3}}$

$=>\ \sqrt{3}(h-7)\ =\ h$

$=>\ (\sqrt{3}-1)h\ =\ 7\sqrt{3}$

$=>\ h\ =\ \dfrac{7\sqrt{3}}{\sqrt{3}-1}$

         = 16.56 m

Hence, the height of the tower is 16.56 m.

Answer 2

Answer:

h=9.58m  / 9.6 (approx)

Explanation:

tan 45=h/x=1

==>h=x

tan 60 =7+h/h =root 3

h(√3-1)=7

h=7/0.73

h=9.58

h=9.6(approx)

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