Q5 of 31 Page 122

From the top of an electric post, two wires are stretched to either side and fixed to the ground, 25 metres apart. The wires make angles 55° and 40° with the ground. What is the height of the post?


Let the height of the post be x metre and distance between post and one of the wire fixed point be y metre.


In right Δ ADC,


AD = y m and CD = x m
CD = tan 55° × y


⇒ x = tan 55° × y


(From table, tan 55° = 1.428 = 1.43)


⇒ x = 1.43 × y …(i)


In right Δ CDB,


BD = AB – AD = (25 –y) m and CD = x


CD = tan 40° × BD


⇒ CD = tan 40° × (25 – y)


(From table, tan 40° = 0.839 = 0.84)


⇒ x = tan 40° × (25 – y)


⇒ x = 0.84 × (25 – y) …(ii)


Dividing eq. (i) from eq. (ii)



⇒ 0.84(25) – 0.84(y) = 1.43(y)


⇒ 1.43(y) + 0.84(y) = 0.84(25)


⇒ 2.27 (y) = 21


⇒ y = 9.25 m
Substituting value of y in eq. (i)


⇒ x = (1.43 × 9.25) m = 13.2275 m


Height of post is 9.25 m


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