Question

the height of a tower is 400m when the altitude of the sun is 30° then the length of its shadow will be​

Answer 1

Given :

• The height of a tower is 400m
• The altitude of the sun is 30°

To Find :

• Length of its shadow

Solution :

As per the given question,

• Let the height of the tower AB = 100m

• The altitude of the sun θ = 30°

• Let the height of the shadow be CB = x

By using the formula,

So we know that AB = 200 , CB = x

⇒ tanθ = AB / CB

⇒ tan30° = 200 / x

⇒ 1/√3 = 200 / x

⇒ x = 200√3

Thus, CB = 200√3

•°• Hence, The length of its shadow is 200√3

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★ More to know :

• tan0° = 0

• tan30° = 1/√3

• tan45° = 1

• tan60° = √3

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Answer 2

$\huge\underline\bold\orange{Answer:-}$

$\large\underline\bold\red{Given:-}$

• Height of a tower $\implies$ 400m when altitude of the sun is 30°

$\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf 400m}\put(2.8,.3){\large\bf }\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\put(3.8,1.3){\large\bf \theta30 }\end{picture}$

$\large\underline\bold\red{To\:Find}$

• Length of shadow of the tower .

$\large\underline\bold\red{Solution}$

Let the height of the tower AB = 200m

Let the height of the shadow be CB = x

By using the formula,

• AB = 200 , CB = x

$\implies$tanθ = $\frac{AB}{CB}$

$\implies$ tan30° = $\frac{200}{x}$

$\implies$$\frac{1}{ \sqrt{3} } \: = \frac{200}{x}$

$\implies$$x \: = 200 \sqrt{3}$

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$\bullet\:\sf Trigonometric\:Values :\\\\\boxed{\begin{tabular}{c|c|c|c|c|c}Radians/Angle & 0 & 30 & 45 & 60 & 90\\\cline{1-6}Sin \theta & 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} & 1\\\cline{1-6}Cos \theta & 1 & \dfrac{\sqrt{3}}{2}& \dfrac{1}{\sqrt{2}}& \dfrac{1}{2}&0\\\cline{1-6}Tan \theta&0& \dfrac{1}{\sqrt{3}}&1&\sqrt{3}&Not D{e}fined\end{tabular}}$