A man observes two verticle poles which are fixed to each other on either side of the road.if width of road is 90feet and heights of pole are in the ratio 1:2,also the angle of elevation of their tops from a point between the line joining the foot of the poles on the road is 60degree.find height of poles.
Answers
The height of the poles are 30√3 feet and 60√3 feet.
Step-by-step explanation:
Referring to the figure attached below, let's make some assumptions
AB = h₁ = height of the first pole
ED = h₂ = height of the second pole
BD = distance between the two poles = 90 feet
Angle of elevation from point C to the top of AB = θ₁ = 60°
Angle of elevation from point C to the top of ED = θ₂ = 60°
Let the distance of point C from the foot of AB be “BC”, then the distance of point C from the foot of ED will be “CD = (90 - BC)”.
Since it is given that the ratio of the heights of the pole are 1:2
So, if the height of the first pole AB is “h1” then the height of the second pole ED will be "h2 = 2h1”.
Now,
Consider ΔABC, applying the trigonometric ratios of a triangle, we get
tan θ₁ = perpendicular/base
⇒ tan 60° = AB/BC
⇒ √3 = h₁/BC
⇒ h₁ = BC√3 ...... (i)
and,
Consider ΔEDC, applying the trigonometric ratios of a triangle, we get
tan θ₂ = perpendicular/base
⇒ tan 60° = ED/CD
⇒ √3 = h₂/(90 - BC)
⇒ 2h₁ = √3 [90 - BC]
⇒ h₁= (√3/2) [90 - BC] ...... (ii)
From (i) & (ii), we get
BC√3 = (√3/2) [90 - BC]
⇒ 2BC = 90 – BC
⇒ 2BC + BC = 90
⇒ 3BC = 90
⇒ BC = 90/3
⇒ BC = 30
Substituting the value of BC in (i), we get
h₁ = BC√3 = 30√3 feet ← height of first pole
∴ h₂ = 2 * h₁ = 2 * 30√3 = 60√3 feet ← height of the second pole
---------------------------------------------------------------------------------------------
Also View:
The angle of elevation of the cloud from a point 60m above the surface of the water of a lake is 30 degree and angle of depression of its Shadow from the same point in a water of lake is 60 degree find the height of the cloud from the surface of water ?
https://brainly.in/question/7405969
Two poles are 200 m apart if from the middle point of the line joining their feet an observer finds the angle of elevation of their tops as 60 and 30 degree respectively then find the ratio of the height of the poles.
https://brainly.in/question/15114546
Angles of elevation of the top of a tower from two points at distance of 9 m and 16 m from the base of the tower in the same side and in the same straight line with it are complementary. Find the height of the tower.
https://brainly.in/question/12389860
