Question

the angle of elevation of the top of the tower at a distance of 120m from point A on thr ground is 45 degree if the angke of elevation of the top of a flagstaff fuxed at the top of the tower, at A is 60 degree then find the height of the flagstaff

Answer 1

Answer,

• Let BC be the tower and CD be the flagstaff. Join C, A and D, A and A, B.
We get two right-angled triangles ABC and BAD which are right-angled at B.
By the problem, it is clear that ∠BAC = 45° and ∠ BAD = 60°.
We use trigonometric ratio tan for both the triangles using BC as height and AB as a base(for ∆ABC) and BD as height and AB as a base(for ∆ABD) to find the height of the flagstaff CD.


Let BC be x.

tan <BAC = BC / AB = x / 120

or,

tan45 ° = x / 120

or,

x = 120

So, we get BC = 120m. In ∆ABD,
tan <BAD = BD / AB = DC + BC / 120 => DC + 120/120

or,

tan 60° = DC + 120/ 120

or,

√3 = DC + 120/ 120

or,

DC = 120 × (√3 - 1 ) = 120 × 0.732

=>>> 87.84

So,

Height of the flagstaff is 87.84 m.

Thanks!!

Answer 2

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• Let BC be the tower and CD be the flagstaff. Join C, A and D, A and A, B.

We get two right-angled triangles ABC and BAD which are right-angled at B.

By the problem, it is clear that ∠BAC = 45° and ∠ BAD = 60°.

We use trigonometric ratio tan for both the triangles using BC as height and AB as a base(for ∆ABC) and BD as height and AB as a base(for ∆ABD) to find the height of the flagstaff CD.

Let BC be x.

tan <BAC = BC / AB = x / 120

or,

tan45 ° = x / 120

or,

x = 120

So, we get BC = 120m. In ∆ABD,

tan <BAD = BD / AB = DC + BC / 120 => DC + 120/120

or,

tan 60° = DC + 120/ 120

or,

√3 = DC + 120/ 120

or,

DC = 120 × (√3 - 1 ) = 120 × 0.732

=>>> 87.84

So,

Height of the flagstaff is 87.84 m.

HOPE SO IT WILL HELP....