Question

Two vertical poles of heights 6 m and 3 m are erected above a horizontal ground AC. Find the value of y.

Answer 1

Answer:

2m

Step-by-step explanation:

ΔPAQ is similar to ΔQRC since,

∠PQA = ∠RQC - vertical angle

∠CRA = ∠PAR - alternate angle

∠APC = ∠PCR - alternate angle

Since ΔPAQ is similar to ΔQRC,

CR/AP = QR/QA = QC/QP = 3/6 = 1/2

∴ QC = QP/2

∴ QC = PC/3 -- (1)

Δ PAC and ΔQBC are also similar since,

∠C is common angle for both

∠CQB = ∠CPA - corresponding angles

∠PAC = ∠QBC = 90

Now, QB/PA = QC/PC --(2)

Substituting (1) in (2) we get,

∴ QB/PA =  (PC/3)/PC

∴ QB/PA = 1/3

∴  y/6 = 1/3

∴ y = 2 m