Question

The angle of elevation of the top of a tower 30m high from the foot of another tower in the same plane is 60 degree and the angle of elevation of the top of the second tower from the foot of the first tower is 30 degree. Find the distance between the two towers and the height of the other tower

Answer 1

Answer:

Distance betweeen the towers is 17.32 meters

Height of the other tower is 10 meters

Step-by-step explanation:

AB is the tower of height 30 m

Let h be the height of the other tower.

In right triangle ABD,

$tan60=\frac{AB}{BD}\\\\\sqrt{3}=\frac{30}{BD}\\\\BD=\frac{30}{\sqrt{3}}........(1)$

In right triangle BCD,

$tan30=\frac{CD}{BD}\\\\\frac{1}{\sqrt{3}}=\frac{h}{BD}\\\\BD=h\sqrt{3}................(2)$

From (1) and (2)

$h\sqrt{3}=\frac{30}{\sqrt{3}}\\\\h=\frac{30}{\sqrt{3}\sqrt{3}}\\\\h=\frac{30}{3}\\\\h=10\: meters$

From (2)

$BD=10\sqrt{3}$

BD=10(1.732)

BD=17.32 meters

Answer 2

Step-by-step explanation:

height of tower is 10m and distance is 10√3m