13. Five mark exercise problems V

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

 

 

Answer:

 

(i) The height of the pole is  \(m\).

 

(ii) The radius of the dome is  \(m\).

 

2. A vertical pole fixed to the ground is divided in the ratio \(1 : 9\) by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a place on the ground, \(25 \ m\) away from the base of the pole, then the height of the pole is $i\sqrt{i}i$.