A ladder leaning against a wall makes an angle θ with the horizontal ground such that cos θ = . If the height of the top of the ladder from the wall is 18 m, then what is the distance ( in m ) of the foot of the ladder from the wall ?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 7.5
The height of the top of the ladder from the foot of the wall is 18 m.
Cosθ = Base/Hypotenuse = 5/13
Let, Base (BC) = 5x and Hypotenuse (AC) = 13x where x is a constant.
Accordingly -
AB = 18 m
From ΔABC -
182 + (5x)2 = (13x)2
182 = 169x2 - 25x2
324 = 144x2
x2 = 324/144
x = 3/2
Base (BC) = 5 × 3/2 = 7.5
The distance of the foot of the ladder from the wall is 7.5 m.