Question

A vertical pole consists of two parts,the lower part being one third of the whole .at a point in the horizontal plane through the base of the pole and distance 20 metres from it the upper part of thecpole substends an angle whose tangent is 1/2 the possible distance

Answer 1

Answer:

$\sf\huge\boxed{Answer:-60 m}$

$\huge\color{red}{Given\:that:-}$

• A vertical pole has two parts.

• The lower part is one third of pole.

• The horizontal plane through the base of the pole and distance is 20 meters.

• Uper part of the pole substends an angle of tangent 1/2 of possible distance.

$\huge\boxed{Explanation:}$

H3cotα=d

 and 

d=150cotφ=60m

 or 

H3d=tanα

 and 

Hd=tanβ

 

tan(β−α)=12=Hd−H3d1+H23d2

+H23d2=4H3d

 

⇒H2−4dH+3d2=0

 

⇒H2−80H+3(400)=0

 

⇒H=20

or 

60m

Answer 2

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