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3 years ago

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A pole that is 3.5m tall casts a shadow that is 1.47m long. At the same time, a nearby tower casts a shadow that is 42.75m long.

How tall is the tower? Round your answer to the nearest meter

1 answer:

Sonja [21]3 years ago

6 0

Answer:

Therefore the height of the tower is 101.79 m.

Step-by-step explanation:

The ratio of the height of an object to the shadow of the object is always constant at certain time.

$\frac{\textrm{The height of object}}{\textrm{The shadow of the object}}= constant$

$\Rightarrow \frac{h_1}{s_1}=\frac{h_2}{s_2}$

Given that,the length of the pole is 3.5 m and it casts a shadow that is 1.47 m long.

The length of shadow that castes by a tower is 42.75 m long.

Here h₁= 3.5 m, s₁=1.47 m, h₂= ? and s₂=42.75 m

$\therefore \frac {3.5}{1.47}=\frac{h_2}{42.75}$

⇒3.5 ×42.75 = h₂× 1.47

$\Rightarrow h_2=\frac{3.5 \times 42.75}{1.47}$

⇒h₂ = 101.79 m (approx)

Therefore the height of the tower is 101.79 m.

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To find all the solutions, we'll give n values of 0, 1, 2,... until x stops belonging to the interval $(0,2\pi)$

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$x=\frac{\frac{2\pi}{3}+2\pi}{5}=\frac{8\pi}{15}$

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For n=2

$x=\frac{\frac{2\pi}{3}+4\pi}{5}=\frac{14\pi}{15}$

$x=\frac{\frac{4\pi}{3}+4\pi}{5}=\frac{16\pi}{15}$

For n=3

$x=\frac{\frac{2\pi}{3}+6\pi}{5}=\frac{4\pi}{3}$

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For n=4

$x=\frac{\frac{2\pi}{3}+8\pi}{5}=\frac{26\pi}{15}$

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For n=5 we would find values such as

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$x=\frac{\frac{4\pi}{3}+10\pi}{5}=\frac{34\pi}{15}$

which don't lie in the interval $(0,2\pi)$

The whole set of results is

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