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Question 2A ladder leaning against a vertical wall makes an angle of 45° with the ground. If the foot of the ladder is 2 m away from the wall, then find the length of the ladder.(Leave your answer in surd form where necessary.)​

Answer»

Refer to the ATTACHMENT for diagram.

Given:

☛ angle that the ladder makes with the ground, θ = 45°

Also,

the ladder makes 90° angle with the WALL so we can IMAGINE it as a RIGHT angled triangle where hypotenuse is the length of the ladder and perpendicular the wall and base be the distance of ladder from the wall.

☛ Distance of ladder from the wall, base = 2 m

To Find:

☛ Length of the ladder

Solution:

In a right angled triangle,

==> cos θ = Base / Hypotenuse

==> cos 45° = 2 / h

==> h = 2 / (1/√2) { since, cos 45° = 1/√2 }

==> h = 2√2

Hence, the length of the wall is 2√2 m


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