Multiple choice

A ladder leaning against a wall makes an angle ( \theta ) with the horizontal ground such that ( \cos \theta = \frac{5}{13} ). If the height of the top of the ladder from the foot of the wall is 18 m, then what is the distance (in m) of the foot of the ladder from the wall?

  1. 19.5

  2. 7.5

  3. 13

  4. 18

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Ladder forms right triangle with wall. Given cosθ = 5/13, and opposite = 18m. Using sin²θ = 1 - cos²θ: sinθ = √(1 - 25/169) = √(144/169) = 12/13. Since tanθ = opposite/adjacent = sinθ/cosθ = (12/13)/(5/13) = 12/5. Let adjacent = x, then 18/x = 12/5, so x = 18 × 5/12 = 7.5m.