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from the base of the tower, you meassure its shadow to be 17.25m.at same the time your shadoe is 0.21m.you are 1.68 tall.how tall ia the tower?(round to two decimal plaves if necessary)

Sagot :

The Solution:

Representing the given in a diagram, we have

By similarity theorem, we have that:

[tex]\frac{BA}{BT}=\frac{BC}{BD}[/tex]

So,

[tex]\begin{gathered} BA=1.68m \\ BT=h=(1.68+x)m \\ BC=0.21m \\ BD=17.25m \end{gathered}[/tex]

Substituting these values in the formula above, we get

[tex]\frac{1.68}{1.68+x}=\frac{0.21}{17.25}[/tex]

Solving for x:

We shall cross multiply,

[tex]0.21(1.68+x)=1.68\times17.25[/tex][tex]0.3528+0.21x=28.98[/tex][tex]0.21x=28.98-0.3528=28.6272[/tex]

Dividing both sides by o.21, we get

[tex]x=\frac{28.6272}{0.21}=136.32\text{ m}[/tex]

The height of the tower is

[tex]h=1.68+x=1.68+136.32=138m[/tex]

Therefore, the correct answer is 138 meters.

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