Advertisements
Advertisements
Question
Two vertical poles of heights 6 m and 3 m are erected above a horizontal ground AC. Find the value of y
Solution
In the ∆PAC and ∆BQC
∠PAC = ∠QBC = 90°
∠C is common
∆PAC ~ QBC
`"AP"/"BQ" = "AC"/"BC"`
`6/y = "AC"/"BC"`
∴ `"BC"/"AC" = y/6` ...(1)
In the ∆ACR and ∆QBC
∠ACR = ∠QBC = 90°
∠A is common
∆ACR ~ ABQ
`"RC"/"QB" = "AC"/"AB"`
`3/y = "AC"/"AB"`
`"AB"/"AC" = y/3` ...(2)
By adding (1) and (2)
`"BC"/"AC" + "AB"/"AC" = y/6 + y/3`
1 = `(3y + 6y)/18`
9y = 18 ⇒ y = `18/9` = 2
The Value of y = 2 m
APPEARS IN
RELATED QUESTIONS
In figure, QA and PB are perpendicular to AB. If AO = 10 cm, BO = 6 cm and PB = 9 cm. Find AQ
In figure, ∠BAC = 90º and segment AD ⊥ BC. Prove that AD2 = BD × DC.
See the given figure. DE || BC. Find AD.
In the given figure, ∠1 = ∠2 and `(AC)/(BD)=(CB)/(CE)` Prove that Δ ACB ~ Δ DCE.
Harmeet is 6 feet tall and casts a shadow of 3 feet long. What is the height of a nearby pole if it casts a shadow of 12 feet long at the same time?
A map is drawn to scale of 1:20000. Find: The area of the lake on the map which has an actual area of 12km2
If ∆ABC – ∆PQR in which ∠A = 53° and ∠Q = 77°, then ∠R is
Which of the following is not a test of similarity?
In figure, if AD = 6cm, DB = 9cm, AE = 8cm and EC = 12cm and ∠ADE = 48°. Find ∠ABC.
In ΔABC, DE || BC (as shown in the figure), If AD = 4 cm, AB = 9 cm and AC = 13.5 cm, then the length of EC is ______.
