Question

the ratio of the length of a tree and it's shadow is 1:1÷root3 the angle of a sun s elevation is

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Answer 1

Solution :-

[ Refer to attachment ]

Length of the tree = BC

Length of the shadow = AB

Angle of sun's elevation = θ

Given :-

Ratio of the length of a tree and it's shadow = 1 : 1/√3

$\implies \dfrac{BC}{AB} = \dfrac{1}{ \dfrac{1}{ \sqrt{3} } }$

$\implies \dfrac{BC}{AB} = 1 \div \dfrac{1}{ \sqrt{3} }$

$\implies \dfrac{BC}{AB} = 1 \times \sqrt{3}$

$\implies \dfrac{BC}{AB} = \sqrt{3}$

From figure,

BC/AC = Side opposite to θ/Side adjacent to θ = = tan θ

Therefore, BC/AC = tanθ

$\implies tan \theta = \sqrt{3}$

$\implies tan \theta = tan60^{ \circ}$

[ Because tan60° = √3 ]

Comparing on both sides

$\implies \theta =60^{ \circ}$

Hence, the angle of sun's elevation is 60°.

Answer 2

$\Large\underline{\underline{\sf{Given}:}}$

• Length of tree : shadow = 1 : 1/√3 .

$\Large\underline\mathfrak{Question}$

• Angle of Elevation of sun From the end point of shadow.

$\Large\underline{\underline{\sf{Solution}:}}$

$\red{\textbf{Refer To image First}} \:$

From image we can see that,

$\textbf{AB = Length of Tree.}$

$\textbf{ BC = Shadow of Tree .}$

$\textbf{Angle ACB = Angle of Elevation of Sun.}$

Now, it is Given that,

$\frac{AB}{BC} = \frac{1}{ \frac{1}{ \sqrt{3} } } \\ \\ \red{\boxed\implies} \: \: \: \frac{AB}{BC} \: = \sqrt{3}$

Now, we know that,,,,

$\tan( \theta) = \frac{perpendicular}{base}$

From our diagram of Right ∆ABC, we have,

AB = Perpendicular

BC = Base ...

and Angle ABC = @ .

So, we can say that,

$\tan( \theta) \: = \frac{AB}{BC} \: \\ \\ or \: \\ \\ \tan( \theta) \: = \sqrt{3} \\ \\ or \\ \\ \tan( \theta) = \tan(60) \\ \\ comparing \: \\ \\ \pink{\large\boxed{\boxed{\bold{ \theta = 60 \degree}}}}$

Hence, angle of Elevation of sun From Corner of shadow to the Top of Tree is 60° ......

$\large\underline\textbf{Hope it Helps You.}$