What is the length of the shadow of a 14 metre high pole when the suns altitude is 60 degree

The height of a tower is 10 m. What is the length of its shadow when Sun's altitude is 45°?

Let BC be the length of shadow is x m

Given that: Height of tower is 10 meters and altitude of sun is 45°

Here we have to find length of shadow.

So we use trigonometric ratios.

In a triangle ABC,

`⇒ tan = (AB)/(BC)`

`⇒ tan 45°=(AB)/(AC)`

`⇒1=10/x`

`⇒x=10`

Hence the length of shadow is 10 m.

Concept: Heights and Distances

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Page 2

If the ratio of the height of a tower and the length of its shadow is `sqrt3:1`, what is the angle of elevation of the Sun?

Let C be the angle of elevation of sun is θ.

Given that: Height of tower is `sqrt3` meters and length of shadow is 1.

Here we have to find angle of elevation of sun.

In a triangle ABC,

`⇒ tanθ =(AB)/(BC)`

`⇒ tan θ=sqrt3/1` ` [∵ tan 60°=sqrt3]`

`⇒ tan θ=sqrt3`

`⇒ θ=60 °`

Hence the angle of elevation of sun is 60°.

Concept: Heights and Distances

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A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.

Let height of the pedestal BD be h metres, and angle of elevation of C and D at a point A on the ground be 60° and 45° respectively.It is also given that the height of the statue CD be 1.6 mi.e., ∠CAB = 60°,∠DAB = 45° and CD = 1.6mIn right triangle ABD, we have

In right triangle ABC, we have

Comparing (i) and (ii), we get

Hence, the height of pedestal

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