Question

From the top of the building 100m high,the angles of the depression of the top and bottom of a tower are observed to be 45° and 60° respectively. Find the height of the tower. Also find the distance between the foot of the building and bottom of the tower.

Answer 1

hope that this will help you.

Answer 2

Answer:

height of the tower = $\frac{100}{\sqrt{3} }$

distance between the building and tower = $\frac{100}{\sqrt{3} } \times (\sqrt{3} -1)$

Step-by-step explanation:

Given, the height of the tower is 100m

We have to find the distance of the building from the tower and the height of the tower.

Since , from the top of the building an elevation of 45° and 60° are made to the top and bottom of the tower respectively.

So,

$tan 60 = \frac{perpendicular}{base}$ = $\frac{100}{x}$

∴ $\sqrt{3}  = \frac{100}{x}$

By solving the above equation ,we gwt;

x = $\frac{100}{\sqrt{3} }$

So, the distance of the tower from the building is  $\frac{100}{\sqrt{3} }$ m .

Now,

$tam 45 = \frac{100 - h}{x}$

$1 = \frac{100-h}{x}$

x = 100 - h

$h = 100 \times \frac{\sqrt{3}-1 }{\sqrt{3} }$

So , h = $\frac{100}{\sqrt{3} } \times (\sqrt{3} -1)$

So, the height of the tower is  h = $\frac{100}{\sqrt{3} } \times (\sqrt{3} -1)$