Question

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?

Answer 1

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.