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?
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Correct Answer: Option D
Explanation:
$$
\begin{array}{ll}
\tan \theta=2.4=\frac{\text { opp }}{\text { adj }} \\
o p p=2.4 \times 5 \\
& l^{2}=50^{2}+120 \mathrm{~cm} \\
l^{2}=2500+14400 \\
l^{2}=\sqrt{16900} \\
l & l=13 \mathrm{~cm} \text { or } 1.3 \mathrm{~m}
\end{array}
$$
$$
\begin{array}{ll}
\tan \theta=2.4=\frac{\text { opp }}{\text { adj }} \\
o p p=2.4 \times 5 \\
& l^{2}=50^{2}+120 \mathrm{~cm} \\
l^{2}=2500+14400 \\
l^{2}=\sqrt{16900} \\
l & l=13 \mathrm{~cm} \text { or } 1.3 \mathrm{~m}
\end{array}
$$