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In Fig. 1, AB is a 6 m high pole and CD is a ladder inclined at an angle of 60° to the horizontal and reaches up to a point D of pole. If AD = 2.54 m, find the length of the ladder. - Mathematics

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In Fig. 1, AB is a 6 m high pole and CD is a ladder inclined at an angle of 60° to the horizontal and reaches up to a point D of pole. If AD = 2.54 m, find the length of the ladder. (use3=1.73)

 

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Solution

In the given figure,

AB = AD + DB = 6 m

Given: AD = 2.54 m

⇒ 2.54 m + DB = 6 m

⇒ DB = 3.46 m

Now, in the right triangle BCD,

`(BD)/(CD)=sin 60^@`

`=>(3.46m)/(CD)=sqrt3/2`

`=>(3.46m)/(CD)=1.73/2`

`=>CD=(2xx3.46m)/1.73`

CD=4 m

Thus, the length of the ladder CD is 4 m.

Concept: Heights and Distances
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