A ladder is placed along a wall such that its upper end is resting against a vertical wall. The foot of the ladder is 2-4 m from the wall and the ladder is making an angle of 68° with the ground. Find the height, upto which the ladder reaches.
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Given :-
Angle of elevation = Ø = 68°
Horizontal distance from wall = x = 2.4 m
To find :-
• Height of the ladder upto which it reaches.
Let the height of ladder = h
This condition forms a ∆ABC.
In ∆ABC,
tanØ = h/x
Putting 'Ø = 68°' and ' x = 2.4 m' in the above equation.
tan 68° = h/2.4
Now finding the value of tan 68° in radians.
For this we just have to multiply the angle Ø with π/180°.
tan 68° = tan(68° × π/180°)
tan 68° = tan(17π/45)
tan 68° = 2.47
Again,
h = 2.4 × 2.47
h = 5.92 m
Hence,
The height upto which ladder reaches = h = 5.92 m
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