A ladder leans against a wall with its foot 2 metres away from the wall and it makes a 40° angle with the ground. How high is the top of the ladder from the ground?

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Solution

Let AC be the ladder which leans against the wall AB.

BC is the distance between the foot of the ladder and the wall.

So, in ΔABC, BC = 2 cm, ∠ABC = 90° and ∠ACB = 40°.

In ΔABC:

⇒ AB = BC × tan 40° … (1)

We know that tan 40° ≈ 0.8391 (From table)

Putting the value in (1):

AB ≈ 2 × 0.8391cm

= 1.6782 cm

Thus, the top of the ladder is at a distance of approximately 1.6782 cm from the ground.

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