Question

Angle of elevation of a ladder leaning against a wall is 60 foot of ladder is 6.5 m find the length of laddder

Answer 1

Hello mate


Good night

Answer 2

✅ See the attachment diagram.

$\begin{gathered} \\ \Large{\bf{\green{\underline{GiVeN\::}}}} \\ \end{gathered}$

Length of ladder (AB) = 6.5 m

Length of foot of the wall (BC) = 2.5 m

$\begin{gathered} \\ \Large{\bf{\pink{\underline{To\:FiNd\::}}}} \\ \end{gathered}$

The height of the wall where the top of the ladder touches it, i.e. the length of AC.

$\begin{gathered} \\ \Large{\bf{\purple{\underline{CaLcUlAtIoN\::}}}} \\ \end{gathered}$

➣ Here ABC is an rightangle triangle.

↝ According to the question hypotenuse & base is given and we calculate the height of the right angle triangle.

$\begin{gathered}\bf\blue{Thus,} \\ \end{gathered}$

$\begin{gathered}\bf\red{According\:to\:Pythagoras\:theorem,} \\ \end{gathered}$

$\begin{gathered}\pink\bigstar\:\:{\underline{\green{\boxed{\bf{\purple{(Hypotenuse)^2\:=\:(Height)^2\:+\:(Base)^2}}}}}} \\ \end{gathered}$

$\begin{gathered}\bf\orange{Where,} \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{(AB)^2\:=\:(AC)^2\:+\:(BC)^2} \\ \\ \end{gathered} :⟹(AB)$

$\begin{gathered}:\implies\:\:\bf{(AC)^2\:=\:(AB)^2\:-\:(BC)^2} \\ \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{(AC)^2\:=\:(6.5)^2\:-\:(2.5)^2} \\ \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{(AC)^2\:=\:42.25\:-\:6.25} \\ \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{(AC)^2\:=\:36} \\ \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{AC\:=\:\sqrt{36}} \\ \\ \end{gathered}$

$\begin{gathered}:\implies\:\:\bf{AC\:=\:\pm\:6} \\ \\ \end{gathered}$

[NOTE ➛ Value of Length is always a positive integer.]

$\begin{gathered}:\implies\:\:\bf\green{AC\:=\:6\:m} \\ \\ \end{gathered}$

$\begin{gathered}\Large\bf\blue{Therefore,} \\ \end{gathered}$

The height of the wall where the top of the ladder touches it is 6 m.