Question

Section V has 3 questions of 5 marks each.
(34.) A person standing between two poles finds that the angles subtended at his eyes by the tops of the
poles is a right angle. If the heights of the two poles are two times and four times the height of the
person and the distance between the two poles is equal to the height of the higher pole, find the ratio
of the distances of the person from the smaller to the bigger poles​

Answer 1

Answer:

Let AB be the men of height h m,

CD and EF be the two towers of height 2h m and 4h m respectively.

∴∠CAE=90o

Draw PQ∥DF passing through A.

⇒CP=PD=h m,QF=h m

∴EQ=3h m

Let DB be d m

∴DB=PA=d m and BF=AQ=(4h−d)m

PAQ is a straight line.

∴∠PAC+∠CAE+∠EAQ=180o

∠PAC+90o+∠EAQ=180o

∴∠PAC+∠EAQ=90o

Let ∠PAC be x.

∴∠EAQ=90o−x   ...(1)

In △CPA,∠PAC=x

⇒∠CPA=90o−x   ...(2)

In △CPA and △AQE

∠PCE=∠EAQ   [each90o−x]

∠CPA=∠EAQ   [each90o]

∴△CPA∼△AQE