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One skyscraper is 100 dm. At some time the shadow of a 1 dm hi

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One skyscraper is $100 d m$ . At some time the shadow of a $1 d m$ high pole is $33 d m$ long from the light of the sun. What will be the angle of elevation of sun and the length of the shadow and the shadow of the skyscraper at the same time.

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One skyscraper is

100 d m

. At some time the shadow of a

1 d m

high pole is

33 d m

long from the light of the sun. What will be the angle of elevation of sun and the length of the shadow and the shadow of the skyscraper at the same time.

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Text solutionVerified

Let

BC

is a skyscraper of height

100 d m

. and

D E

is a pole of height

9 d m

.
Let elevation angle of sun is

θ

.
According to question,

∠ D A E = ∠ C A B = θ

and

A E = 33 d m

From right angled

Δ D E A

tan θ = \frac{D E}{A E}

= \frac{9}{3 3}

= 3

= tan 6 0^{0} = θ = 6 0^{0}

Hence, angle of elevation of sun

= 6 0^{0}

Again from right angled

Δ A BC

tan θ = \frac{BC}{A B}

tan 6 0^{0} = \frac{100}{A B}

3 = \frac{100}{A B}

A B = \frac{100}{3}

Hence, angle of elevation of sun is

6 0^{0}

and length of shadow of skyscraper

\frac{100}{3}

decimeter.

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Question Text	One skyscraper is $100 d m$ . At some time the shadow of a $1 d m$ high pole is $33 d m$ long from the light of the sun. What will be the angle of elevation of sun and the length of the shadow and the shadow of the skyscraper at the same time.
Answer Type	Text solution:1
Upvotes	150

One skyscraper is 100dm. At some time the shadow of a 1dm high pole is 33​dm long from the light of the sun. What will be the angle of elevation of sun and the length of the shadow and the shadow of the skyscraper at the same time.

Text solutionVerified

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One skyscraper is $100 d m$ . At some time the shadow of a $1 d m$ high pole is $33 d m$ long from the light of the sun. What will be the angle of elevation of sun and the length of the shadow and the shadow of the skyscraper at the same time.