Question

A man walks 10m towards the lamp post and notices that the angle of elevation of the top of the post increases from 30 - 45 degrees the height of the lamp post is

Answer 1

Answer:

Step-by-step explanation:

Take the tangent,

Tan45 = AB/BD = h/x

=> 1 = h/x

=> h = x.

Now Tan30° = AB/BC = h/10+x

=> 1/√3 = h/10+x

Substitute h = x in the above equation

=> 10+x = x√3

=> x(√3-1) = 10

=> x = 10/√3-1 = 10(√3+1)/(√3-1)(√3+1) = 5(√3+1)

Thus height of lamp post = 5(√3+1) m.