Question

A Technician has to
repair a light on a pole
of height 10 m. She
needs to reach a point 1
m below the top of the
pole to undertake the
repair work. What
should be the length of
the ladder that she
should use which, when
inclined at an angle
of 60° to the ground,
would enable her to
reach the required
position? Also, how far
from the foot of the pole
should she place the
foot of the ladder?​

Answer 1

For diagram Refer to image first.

From image we have given that :-

• AB = Pole = 10m.
• Point C = where she needs to reach .
• AC = 1m .
• ∠CDB = 60°
• CD = Length of ladder .
• BD = distance between foot of the pole and foot of the ladder .

To Find :-

• CD .
• BD .

Solution :-

→ AB = 10m.

→ AC = 1m.

So,

→ CB = AB - AC

→ CB = 10 - 1 = 9m .

Now, in Right ∆ABC ,

→ CB = 9m.

→ ∠CDB = 60°

So,

→ Tan(∠CDB) = Perpendicular / Base

→ Tan60° = CB / BD

Putting value of Tan60° = √3, we get,

→ √3 = (9/BD)

→ BD = (9/√3)

Rationalising the RHS part ,

→ BD = (9/√3) * (√3/√3)

→ BD = (9√3)/3

→ BD = 3√3 m . (Ans.)

Similarly,

→ sin(∠CDB) = Perpendicular / Hypotenuse

→ sin60° = CB / CD

Putting value of sin60° = (√3/2), we get,

→ (√3/2) = 9/CD

→ CD = (9*2)/√3

→ CD = (18/√3)

→ CD = (18√3/3)

→ CD = 6√3 m. (Ans.)

Hence, Length of ladder is 6√3m and distance between foot of the pole and foot of the ladder is 3√3m.

Answer 2

Answer:

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