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In DelatOPQ , right - angled at P , OP =...

In `DelatOPQ` , right - angled at P , OP = 7 cm and OQ - PQ =1 cm . Determine the values of sinQ and cos Q .

Text Solution

Verified by Experts

Let PQ =x cm
`:. OQ=(x+1)`cm
in `DeltaOPQ`,
From Pythagoras theorem
` OQ^(2)=OP^(2)+PQ^(2)`
`rArr (x+1)^(2)=7^(2)+x^(2)`
`rArr x^(2)+2x+1=49+x^(2)`
`rArr 2x=48`
`rArr x=24`
`:. x+1=24+1=25`
Thus, `PQ=24cmand OQ =25cm`
Now , `sin Q = (OP)/(OQ)=(7)/(25)`
`cosQ=(PQ)/(OQ)=(24)/(25)`
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