Question

A flag pole 'h' metres is on the top of hemispherical dome of radius "r" meters. A man is standing 7m away from the dome. Seeing the top of the pole at an angle 45° and moving 5m away from the dome and seeing the bottom of the pole at an angle 30°. Find
(i) the height of the pole
(ii) radius of the dome.
($\sqrt{3} = 1.732$)
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Answer 1

Answer:

(i) 7 m

(ii) 16.392 m

Step-by-step explanation:

When he moves back more 5 m, angle at which he can see is 30°.

In that imaginary triangle,

= > tan30° = r / ( r + 7 + 5 )

= > 1/√3 = r/( r + 12 )

= > r + 12 = r√3

= > 12 = r( √3 - 1 )

= > 12 = r( 1.732 - 1 )

= > 12 = r(0.732)

= > 12/0.732 = r

= > 16.392 = r

Radius of dome is 16.392 m.

In triangle where man is only 7 m away from dope,

= > tan45° = ( r + h ) / ( r + 7 )

= > 1 = ( r + h ) / ( r + 7 )

= > r + 7 = r + h

= > 7 = h