Question

Question 2
A 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 1

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

Answer 2

Answer:

2√2

Step-by-step explanation:

Length (l) of the ladder is

l² = 2² + 2² = 8

l = √8 = 2√2

==========

2 / l = cos45°

l = 2 / cos45°

l = 2(2/√2) = 4 / √2 = 2√2