An observer in a stationary balloon at a height of 700 m above a level plain in the rear of a front line trench, looks down at the trench and sees the angle of depression 30°. He then sights an enemy machine gun beyond the trench at an angle of depression 60°. How far is the gun from the trench?
Answers
Given : An observer in a stationary balloon at a height of 700 m above a level plain in the rear of a front line trench, looks down at the trench and sees the angle of depression 30°. He then sights an enemy machine gun beyond the trench at an angle of depression 60°
To Find : How far is the gun from the trench
Solution:
Angle of depression = angle of elevation
Tan 30 ° = ( height of balloon ) / ( horizontal distance of trench )
=> 1/√3 = 700 / horizontal distance of trench
=> horizontal distance of trench = 700 √3 m
Tan 60 ° = ( height of balloon ) / ( horizontal distance of machine gun )
=> √3 = 700 / horizontal distance of of machine gun
=> horizontal distance of of machine gun = 700/√3 m
Distance between machine gun & trench = 700 √3 - 700/√3
= 700 (√3 - 1/√3)
= 700( 3 - 1)/√3
= 1400/√3
= 808.3 m
Learn more:
The angle of elevation of top of a pole from two points A and B on ...
https://brainly.in/question/11520026
the angle of elevation of a vertical Tower observed from the age of a ...
https://brainly.in/question/12120882
if the angle of elevation of the sun is 60° then the ratio of the height ...
https://brainly.in/question/9365148