Question

Find the angle of depression of stick leaning against a wall of length 13m and the foot of the ladder is 6.5m from the wall.
30°​

Answer 1

Correct Question is

• Find the angle of depression of ladder leaning against a wall of length 13m and the foot of the ladder is 6.5m from the wall.

$\large\underline{\sf{Solution-}}$

Let AB be the wall and AC be the ladder leaning against the wall such that its top touches the wall at A and foot of ladder touches the ground at C.

So,

• Length of Ladder, AC = 13 m

• Distance of foot of ladder from the bottom of the wall, BC = 6.5 m

Let

• The angle of depression be 'θ'.

Now,

$\rm :\longmapsto\:In \: \triangle \: ABC$

$\rm :\longmapsto\: cos \: \theta \: = \: \dfrac{BC}{AC}$

$\rm :\longmapsto\: cos \: \theta \: = \:\dfrac{6.5}{13}$

$\rm :\longmapsto\: cos \: \theta \: = \:\dfrac{1}{2}$

$\rm :\longmapsto\: cos \: \theta \: = \:cos60 \degree$

$\rm :\implies\:\theta \: = \: 60 \degree$

Additional Information

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0\end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$