Two pillars of equal height are on either side of a road which is hundred metre wide the angles of elevation of the top of the pillars are 60 degree and 30 degree at a point on the road between the pillars then the point between the pillars divide the road in the ratio..
Answers
Answer:
simple mate....pls rotate tje picture for your convinience.
Step-by-step explanation:
43.301 m
Step-by-step explanation:
Refer the attached figure
Let the height of the pillars i.e. AB and DE be h
In ΔABC
Tan\theta = \frac{Perpendicular}{base}Tanθ=
base
Perpendicular
Tan 60^{\circ}= \frac{AB}{BC}Tan 60
∘
=
BC
AB
\sqrt{3}= \frac{h}{x}
3
=
x
h
\sqrt{3}x= h
3
x=h ---1
In ΔCDE
Tan\theta = \frac{Perpendicular}{base}Tanθ=
base
Perpendicular
Tan 30^{\circ}= \frac{DE}{CD}Tan 30
∘
=
CD
DE
\frac{1}{\sqrt{3}}= \frac{h}{100-x}
3
1
=
100−x
h
\frac{1}{\sqrt{3}}(100-x)= h
3
1
(100−x)=h --2
Equate 1 and 2
\sqrt{3}x= \frac{1}{\sqrt{3}}(100-x)
3
x=
3
1
(100−x)
x=25x=25
So, Height of pillars = AB = \sqrt{3}(25)= 43.301
3
(25)=43.301
Hence the height of pillar is 43.301 m.
