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Q.

A ladder leaning against a vertical wall, makes an angle of 60∘ with the ground. The foot of the ladder is 3.5 𝑚
away from the wall. Find the length of the ladder.

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a

7 𝑚

b

10 𝑚

c

15 𝑚

d

25 𝑚

answer is A.

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Detailed Solution

According to the diagram,
Question Image

Question Image

𝐵𝐶 is the distance from the wall = 3.5 𝑚. And, let 𝐴𝐶 be the ladder with length = 𝑥 𝑚.
The ladder makes an angle of 60∘ with the ground. Therefore, 𝑐𝑜𝑠 60∘ = 𝐵𝐶
𝐴𝐶
⇒ 1 = 3.5
2 𝑥
⇒ 𝑥 = 3.5 × 2
⇒ 𝑥 = 7 𝑚
Therefore, the length of the ladder is: 𝐴𝐶 = 𝑥 = 7 𝑚.

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