The angle of elevation of the top of a tower at any point A on the ground is 15degree on walking 100ft towards the tower the angle of elevation becomes 30degree . Find the height of the tower.
Answers
Answer:
the height of the tower. = 50 m
Step-by-step explanation:
The angle of elevation of the top of a tower at any point A on the ground is 15degree on walking 100ft towards the tower the angle of elevation becomes 30degree . Find the height of the tower.
Tan 15° = Height of Tower/Distance of A from Base of Tower
=>Height of Tower = Distance of A from Base of Tower * Tan 15°
Tan 30° = Height of Tower/ (Distance of A from Base of Tower - 100)
=> Height of Tower = (Distance of A from Base of Tower - 100)Tan 30°
(Distance of A from Base of Tower - 100)Tan 30° = Distance of A from Base of Tower * Tan 15°
=> Distance of A from Base of Tower( Tan 30 - Tan 15) = 100Tan30
=> Distance of A from Base of Tower = 100Tan30/( Tan 30 - Tan 15)
Tan 30 = 1/√3 Tan 15 = 2 - √3
Height of Tower = Distance of A from Base of Tower * Tan 15°
=> 100Tan30Tan 15° /( Tan 30 - Tan 15)
=> 100(2 - √3) /(1 - 2√3 +3)
=> 100( 2 - √3)/(4 -2√3 )
= 50
the height of the tower. = 50 m