Question

A ladder leans against a vertical wall at an angle 60 and the height of the wall is 12m, calculate the length of the ladder.

Answer 1

Given that ,

Height of wall = 12 m

Angle b/w wall and ladder = 60°

We know that ,

$\large \sf \fbox{ Sin( \theta) = \frac{P}{H} }$

Thus ,

$\sf \mapsto Sin( 60) = \frac{12}{Length \: of \: ladder } \\ \\ \sf \mapsto \frac{ \sqrt{3} }{2} = \frac{12}{Length \: of \: ladder} \\ \\ \sf \mapsto Length \: of \: ladder = \frac{24}{ \sqrt{3} } \\ \\ \sf \mapsto Length \: of \: ladder = \frac{24 \sqrt{3} }{3} \\ \\ \sf \mapsto Length \: of \: ladder = 8 \sqrt{3} \: \: m$

$\sf \therefore \underline{The \: length \: of \: ladder \: will \: be \: 8 \sqrt{3} \: \: m}$

Answer 2

Answer:

Length of ladder= 13.85641 m

Explanation:

The leangth of the ladder is the hypotinuse or can be denoted as 'c'. Whereas the height of the vertical wall is called opposite or can be denoted as 'a'

a= 12 m

c =  a /sin(α)

c =   12/sin(12)

c = 13.85641 m