Question

two poles of equal heights are on 2sides of highway 30m abide. the angle of elevation of the top of 2 poles from a point between them are such that their tangent ratios are 1 and 1/2 find their height?​

Answer 1

Answer:

43.25

Step-by-step explanation:

Let AB and CD be the two poles and M be the point where the angle of elevation is made of 30

0

and 60

0

respectively.

Let the road CM =x m and AM =100−x m

In right angled △MCD, we have

tan60

0

=

CM

DC

⇒

3

=

x

h

⇒h=x

3

(i)

In right angled △MAB, we have

⇒tan30

0

=

AM

BA

⇒

3

1

=

100−x

h

⇒h

3

=100−x

⇒(x

3

)

3

=100−x ....(from {i})

⇒3x=100−x

⇒4x=100

⇒x=25 m

Therefore, height of pole CD,

⇒CD=25×1.732

⇒CD=43.25m

Thus, height of each pole is 43.25 m.