Question

two pillar of equal height and on either side of a road which is 100m wide . the angle of elevation of the top of the pillars are 60 and 30 at a point in the road between the pillars. find the position of the point between the pillars and the height of each pillar​

Answer 1

Given:

✭ Pillars are of equal height

✭ Width of road is 100 m

✭ Angle of elevation to first tower = 60°

✭ Angle of elevation to second tower = 30°

To Find:

◈ Position of point between the pillars

◈ Height of each pillar

Solution:

Let

• The towers be AB and ED
• BC = x m

Hence,

➝ CD = 100 - x m

Consider ΔABC

»» tan 60° = AB/x

»» √3 = AB/x

»» AB = √3x -eq(1)

Consider ΔEDC

➢ tan 30° = ED/CD

➢ 1/√3 = ED/100-x

➢ ED = (100 - x)/√3 -eq(2)

By given, LHS of equation 1 and 2 are equal

Hence,

➳ √3 x = (100-x)/√3

➳ 3x = 100-x

➳ 4x = 100

➳ x = 25m

Hence,

The point is 25m from first tower and 75 m from second tower

✪ The height of the tower AB = ED

⪼ AB = ED = 25√3 m

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Answer 2

Hoping my attachment is clear and it helps you