A ladder makes an angle of $60^o$ with the ground when placed against a wall. If the foot of the ladder is 2 m away from the wall, then the length of the ladder is-
$
{\text{A}}.\;\dfrac{4}{{\sqrt 3 }}\;{\text{m}} \\
{\text{B}}.\;4\sqrt 3 \;{\text{m}} \\
{\text{C}}.\;2\sqrt 2 \;{\text{m}} \\
{\text{D}}.\;4\;{\text{m}} \\
$
VerifiedHint: The angle of elevation is the angle above the eye level of the observer towards a given point. The angle of depression is the angle below the eye level of the observer towards a given point. The cosine function is the ratio of the adjacent side and the hypotenuse.
Complete step-by-step answer:
Let the ladder DE be of the length x. The base of the ladder E is at a distance of 2 m from C as shown, where DC is the vertical wall. We will apply trigonometric formulas in triangle DCE as follows-
\[ In\;\vartriangle DCE,\]
$ \;\cos {60^{\text{o}}} = \dfrac{{CE}}{{DE}} $
$ \dfrac{1}{2} = \dfrac{2}{{\text{x}}} $
\[ {\text{x}} = 4\;{\text{m}} \]
This is the length of the ladder, the correct option is D. 4 m
Note: In such types of questions, it is important to read the language of the question carefully and draw the diagram step by step correctly. When the diagram is drawn, we just have to apply basic trigonometry to find the required answer.
