Math, asked by Anonymous, 10 months ago

The length of the shadow of a tree is 10√3m. when the angle of elevation of the sun is 60° . what is the length of the shadow of the tree when the angle of elevation is the sum is 30°?

Answers

Answered by Anonymous

49

Answer:

$\huge\bf\underline\purple{Question}$

The length of the shadow of a tree is 10√3m. when the angle of elevation of the sun is 60° . what is the length of the shadow of the tree when the angle of elevation is the sum is 30°?

$\huge\bf\underline\red{Solution:}$

Let the height of the tree be x

$\bf\orange{ In\: ABC}$

$\bf\orange{ tan\: 60° = \frac{h}{BC} }$

$\bf\orange{\because h = \sqrt{3} \times 10 \sqrt{3} }$

$\bf\orange{\implies 30 \:m}$

Now in ∆ABD,

$\setlength{\unitlength}{1.5cm}\begin{picture}(6,2)\linethickness{0.5mm}\put(7.7,2.9){\large\sf{A}}\put(7.7,1){\large\sf{B}}\put(10.6,1){\large\sf{C}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){1.9}}\qbezier(10.5,1)(10,1.4)(8,2.9)\put(7.2,1.9){\sf{\large{h}}}\put(9,0.7){\sf{\large{b}}}\put(9.4,2){\bf{ \underline {Venomanish01} }}\put(8.2,1){\line(0,1){0.2}}\put(8,1.2){\line(3,0){0.2}}\put(8.1,1.7){\bf{Tree}}\end{picture}$

$\bf\orange{ tan\: 30° = \frac{AB}{BD} = \frac{h}{x} }$

$\bf\orange{\implies \frac{1}{ \sqrt{3}} = \frac{30}{x} }$

$\bf\orange{x = 30 \sqrt{3} \:m}$

____________________________________

Hope it will be helpful :) .....✍️

Answered by Anonymous

6

$\huge\star\underline\mathtt\purple{Answer:-}$ $<body bgcolor = lavender><marquee direction = "up"><font color = blue>$

Let the height of the tree be x.

In ABC,

tan60° = $\frac{h}{BC}$

Therefore, h = √3 × 10√3

= 30m

Now in ∆ABC,tan 30° = $\frac{AB}{BD}$ = $\frac{h}{x}$

= $\frac{1}{√3}$ = $\frac{30}{x}$

x= 30√3m

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