A ladder leaning against a wall makes an angle ? with the horizontal ground such that sin? =12/13. If the foot of the ladder is 7.5m from the wall, then what is the height of the point where the top of the ladder touches the wall?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 18 m
Let AB be the ladder.
In the right angle triangle ABC,
sinϴ = AC/AB = 12/13
cosϴ = (1 - 144/169)½ = (25/169)½ = 5/13
⇒ tanϴ = AC/BC = 12/5
⇒ AC = (12/5) × 7.5 = 18
so the height of the point where the top of the ladder touches the wall = 18 m