A ladder rests against a vertical wall and makes an angle θ with the horizontal ground such that tan θ = 5/12. If the length of the ladder is 13 meters, find the height at which the ladder touches the wall.
Show answer & explanation
Correct answer: C
Explanation
Given:
tan θ = 5/12
Length of the ladder = 13 meters
By the formula:
tan θ = opposite side / base
sin θ = opposite side / hypotenuse
tan θ = 5/12 ⇒ sides of the triangle 5 : 12 : 13
sin θ = 5/13
Height = 13 × (5/13) = 5
Height on the wall = 5 meters