The angle of elevation of the top of a tower at a point on the ground is 30 degree . If the height of the tower is tripled, find the angle of elevation of the top of the same point. .
Answers
Answer:
60 degree
Step-by-step explanation:
The angle of elevation of a tower at the point on the ground is 30 degree .
Refer the attached figure
Let the height of the tower be h
So, AB = h
Base = BC
In \triangle{ABC}△ABC
Tan\theta = \frac{Perpendicular}{Base}Tanθ=
Base
Perpendicular
Tan 30^{\circ} = \frac{AB}{BC}Tan30
∘
=
BC
AB
\frac{1}{\sqrt{3}} = \frac{h}{BC}
3
1
=
BC
h
BC=\sqrt{3}hBC=
3
h
Now the height is tripled Find the angle of elevation the top at the Same point
Tan\theta = \frac{Perpendicular}{Base}Tanθ=
Base
Perpendicular
Tan\theta = \frac{3h}{\sqrt{3}h}Tanθ=
3
h
3h
Tan\theta = \frac{3}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}Tanθ=
3
3
×
3
3
Tan\theta = \frac{3\sqrt{3}}{3}Tanθ=
3
3
3
\theta = 60^{\circ}θ=60
∘
Hence the angle of elevation the top at the Same point is 60°