The angle of elevation of the top of a tower at a point on the ground is 30°. What will be the angle of elevation, if the height of the tower is tripled?
Answers
Answered by
5
Angle of elevation will change to 60 degrees.
Step-by-step explanation:
We find that ABC is a triangle with AB as the hypotenuse and angle C is 90 degrees. Given that angle B is 30 degrees. Let x be the height of the tower initially. This will not change the distance BC.
AC = opposite = x
BC = adjacent
tan 30 = opposite / adjacent = x/adjacent
1/√3 = x/adjacent
So adjacent = x√3 -----(1)
When height of tower changes:
tan B = 3x/ adjacent = 3x / x√3 = √3
tan 60 = √3
Therefore angle B = 60 degrees
Angle of elevation will change to 60 degrees.
Similar questions