Answer:
Therefore the height of the tower is 116.75 m.
Step-by-step explanation:
Given that a pole that is 2.6 m tall casts a shadow that is 1.03 m long.
Here the height of a object directly proportional to the shadow. It means
Height of the object ∝ shadow
Height of the object= k.shadow
[k is the proportional constant.]
[tex]\Rightarrow \frac{h}{s} =k[/tex] [Height of object is denoted by h and shadow is denoted by s]
Then,
[tex]\frac{h_1}{s_1} =k[/tex] [h₁ is the height of the pole and s₁is the length of the shadow]
Again for the tower
[tex]\frac{h_2}{s_2}=k[/tex] [h₂ is the height of the tower and s₂ is the length of the shadow]
Therefore,
[tex]\frac{h_1}{s_1}=\frac{h_2}{s_2} =k[/tex]
[tex]\Rightarrow\frac{h_1}{s_1}=\frac{h_2}{s_2}[/tex]............(1)
Given [tex]h_1 = 2.6 m[/tex] ,[tex]s_1=1.03m[/tex] and [tex]s_2=46.25m[/tex]
Putting the value of [tex]h_1,s_1[/tex] and [tex]s_2[/tex] equation (1)
[tex]\frac{2.6}{1.03}=\frac{h_2}{46.25}[/tex]
[tex]\Rightarrow h_2 \times1.03= 2.6\times 46.25[/tex] [cross multiplication]
[tex]\Rightarrow h_2 = \frac{2.6\times 46.25}{1.03}[/tex]
[tex]\Rightarrow h_2= 116.75[/tex]
Therefore the height of the tower is 116.75 m.
