Question

If two towers of height H1 and H2 subtend angle of 60 degree and 30 degree respectively ,at the midpoint of the line joining their feet,then H1 : H2 is

Answer 1

Answer:

here's your answer in the picture

Answer 2

Given: If two towers of height H1 and H2 subtend angle of 60 degree and 30 degree respectively, at the midpoint of the line joining their feet

To find: The value of H1:H2.

Solution:

Let the distance between the poles and the mid-point be x. If a line is drawn from the top of the towers to the mid-point on the ground, two right-angled triangles are formed where x forms the base in both the triangles.

For the tower with height H1, the following equation is formed.

$tan 60 = \frac{H1}{x}$

$\sqrt{3} = \frac{H1}{x}$

$H1 = x\sqrt{3}$

For the tower with height H2, the following equation is formed.

$tan 30 = \frac{H2}{x}$

$\frac{1}{\sqrt{3} } = \frac{H2}{x}$

$H2 = \frac{x}{\sqrt{3} }$

The ratio of H1 to H2 is calculated as follows.

$\frac{H1}{H2} = \frac{x\sqrt{3} }{x/\sqrt{3} }$

     $= \frac{3}{1}$

$H1:H2 = 3:1$

Therefore, the value of H1:H2 is 3:1.