A ladder resting on a vertical wall makes an angle whose tangent is \(2.4\) with the ground. If the distance between the foot of the ladder and the wall is \(50 \mathrm{~cm}\), what is the length of the ladder?
A. \(1.1 \mathrm{~m} \quad\) B. \(1.2 \mathrm{~m} \quad\) C. \(9 \mathrm{~m} \quad\) D. \(1.3 \mathrm{~m}\)
Correct Answer: D
Explanation
$$ \begin{array}{ll} \tan \theta=2.4=\frac{\text { opp }}{\text { adj }} \\ o p p=2.4 \times 5 \\ & l^{2}=50^{2}+120 \mathrm{~cm} \\ l^{2}=2500+14400 \\ l^{2}=\sqrt{16900} \\ l & l=13 \mathrm{~cm} \text { or } 1.3 \mathrm{~m} \end{array} $$
