Answer :
Answer:
The tower is 73.4 m tall
Step-by-step explanation:
The height of the pole = 2.5 m
The shadow cast by the pole = 1.72 m
Shadow cast by tower = 50.5 m
To find the height of the tower, we proceed by finding the angle of elevation, θ, of the light source casting the shadows as follows;
[tex]Tan\theta =\dfrac{Opposite \ side \ to\ angle \ of \ elevation}{Adjacent\ side \ to\ angle \ of \ elevation} = \dfrac{Height \ of \ pole }{Length \ of \ shadow} =\dfrac{2.5 }{1.72}[/tex]
[tex]\theta = tan ^{-1} \left (\dfrac{2.5 }{1.72} \right) = 55.47 ^{\circ}[/tex]
The same tanθ gives;
[tex]Tan\theta = \dfrac{Height \ of \ tower}{Length \ of \ tower \ shadow} =\dfrac{Height \ of \ tower }{50.5} = \dfrac{2.5}{1.72}[/tex]
Which gives;
[tex]{Height \ of \ tower } = {50.5} \times \dfrac{2.5}{1.72} = 73.4 \ m[/tex]