A ladder 7.60 m long leans against an exterior wall. If the ladder is inclined at an angle of 68.0° to the horizontal, what is the horizontal distance from the bottom of the ladder to the wall (in m)? m

2.85 m

Explanation:

From trigonometry,

Cosine = Adjacent/Hypotenuse

Assuming, The wall, the ladder and the ladder forms a right angle triangle as shown in fig 1, in the diagram attached below.

cos∅ = a/H Equation 1

Where ∅ = Angle the ladder makes with the horizontal, a = The horizontal distance from the bottom of the ladder to the wall, H = The length of the ladder.

make a the subject of the equation

a = cos∅(H) Equation 1

Given: ∅ = 68 °, H = 7.6 m.

Substitute into equation 2

a = cos(68)×7.6

a = 0.375×7.6

a = 2.85 m.

Hence the horizontal distance from the bottom of the ladder to the wall = 2.85 m

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