Answer:
height of building,H = 5.5 ft + 105.2 ft = 111 ft to the nearest ft.
Step-by-step explanation:
in this question we have given angle of elevation=[tex]70^o[/tex]
when surveyor walks 50m farther from the base of the tower that time angle of elevation=[tex]50^o[/tex]
As shown in figure in triangle ABD
[tex]Tan (70)= \frac{h}{x} [/tex]
.............(1)
or h=2.74x
and in triangle ABC
[tex] Tan (50)= \frac{h}{50+x} [/tex]
...........(2)
put value of h in equation 2
we got,
[tex] 1.19= \frac{2.74x}{50+x} [/tex]
[tex](50+x)1.19=2.74x\\50\times 1.19+1.19x-2.74x=0\\59.5-1.55x=0\\59.5=1.55x\\x=38.39ft[/tex]
therefore,
Height of the tower is,h=2.74\times 38.39ft
h=105.2ft
Therefore,
height of building,H = 5.5 ft + 105.2 ft = 111 ft to the nearest ft.
