Question

From a point P on the ground the angle of
elevation of the top of a 10 m 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 P is 45°. Find the
length of the flagstaff and the distance of
the building from the point P. (You may
take root 3 = 1.732)​

Answer 1

$\huge\mathbb{↑↑SOLUTION↑↑}$

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Hope it helps uh!!!

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Answer 2

$\Large{\underline{\underline{\bf{\blue{Given}}}}}$

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

$\Large{\underline{\underline{\bf{\blue{To\:find}}}}}$

Find thel ength of the flagstaff and the distance of the building from the point P.

$\Large{\underline{\underline{\bf{\blue{Solution}}}}}$

• BA = building = 10m
• BC = flag staff = x

★ In triangle ∆BAP ★

$\implies\sf tan30\degree=\Large\frac{BA}{AP}$

$\implies\sf \Large\frac{1}{\sqrt{3}}=\Large\frac{10}{AP}$

$\implies\sf AP=10\sqrt{3}=10\times{1.732}=17.32m$

★ Now, In ∆APC ★

$\implies\sf tan45\degree=\Large\frac{AC}{AP}$

Putting the value of AP

$\implies\sf 1=\Large\frac{10+x}{17.32}$

$\implies\sf 17.32=10+x$

$\implies\sf x=17.32-10=7.32m$

Hence,

• The length of flag staff = 7.32m
• Distance of the building from point P = 17.32m

$\Large{\underline{\underline{\bf{\blue{Trigonometric\:ratios}}}}}$

• tan0° = 0
• tan30° = 1/√3
• tan45° = 1
• tan60° = √3
• tan90° = not defined