Question

angle of elevation of a ladder leaning against the wall is 60 degree and the foot of the ladder is 9.5m away from the wall. Find the length of the ladder.

Answer 1

Define x:

Let the length of the ladder be x

Find the length of the ladder:

cos θ = adj/hyp

cos (60) = 9.5/x

x = 9.5/cos(60)

x = 9.5/0.5

x = 19 m

Answer: The length of the ladder is 19 m

Answer 2

let the length of the ladder be ' x '

given, that the foot of the ladder is 9.5 m away from the wall.

base length between the wall and ladder

= 9.5 m

the length of the ladder from the bottom to the top of wall

= x = hypotenuse ( in ∆ )

since , we have given base length between to objects , so then as we know that cos A is max. at ( 0 ) , it means it lies on the base ( straight line ) , the foot of the ladder makes an angle of 60 ° with the top of wall.

as we know that ,

cosA = base / hypotenuse

here, A = 60° , base ( given ) = 9.5 m ,

hypotenuse = x ( required length of ladder )

cos 60° = 9.5 / x

1 / 2 = 9.5 / x

x = 9.5 × 2 = 19 m

therefore , length of the ladder = 19 m

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Your Answer : length = 19 m
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