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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