Math, asked by jjaggeshv, 9 months ago

The shadow of a tower standing on a level ground is found to be 40m longer when the sun's altitude is 30 than when it is 60 find the height of the tower ​

Answers

Answered by dplincsv
11

Step-by-step explanation:

Refer the attachment

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Answered by Anonymous
4

Step-by-step explanation:

Solution :

Let the AB be the height of a tower.

DC = 40 m

DB is 40 m longer than BC.

Therefore,

DB = DC + BC

________________

In ∆ABC,

tan 60° = AB/BC

√3 = AB/BC (∵ tan 60° = √3)

√3 BC = AB (Taking BC to the left hand side)

BC = AB/√3..........[Equation (1)]

________________

In ∆ABD,

tan 30° = AB/BD

1/√3 = AB/BD

BD = √3 AB

DC + BC = √3 AB (∵√3 AB DB = DC + BC)

BC = √3 AB - DC

BC = √3 AB - 40 m......[Equation (2)] (∵ It is given that DC = 40 m)

__________________....

★ From Equation (1) and (2) we get,

BC = BC

AB/√3 = √3 AB - 40

AB = √3 (√3 AB) - 40√3 (Taking √3 to the RHS)

AB = 3 AB - 40√3

40√3 = 3AB - AB

40√3 = 2AB

AB = 40√3/2

AB = 20√3 m

or

AB = 20 (1.732) (Taking the value of √3 = 1.732)

AB = 34.64 m

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