Question

From a point P on the ground the angle of elevation of the top of a 10m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from point P is 45°. Find the length of the flagstaff and the distance of the building from the point P.

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Answer 1

Answer:

Flagstaff= 7.32 m

Distance of building from point P = 17.32 m

Step-by-step explanation:

Refer to the attachment...

Answer 2

$\huge{\underline{\mathrm{\blue{Answer-}}}}$

Distance of the building from point P is 17.32 m.

Length of flagstaff = 7.32 m

$\huge{\underline{\mathrm{\blue{Explanation-}}}}$

In ∆PAB,

Tan30° = $\sf{\dfrac{AB}{AP}}$

$\implies$ $\sf{\dfrac{1}{\sqrt{3}}\:=\:\dfrac{10}{AP}}$

$\implies$ AP = 10√3

$\implies$ AP = 10 × 1.73

$\implies$ AP = 17.32 m

$\therefore$ Distance of the building from point P is 17.32 m.

Now, let's suppose DB = x m.

AD = (10+x) m.

In ∆PAD,

Tan45° = $\sf{\dfrac{AD}{AP}}$

$\implies$ 1 = $\sf{\dfrac{10+x}{10\sqrt{3}}}$

$\implies$ x = 10(√3-1)

$\implies$ x = 7.32 m

$\therefore$ Length of flagstaff = 7.32 m