In the diagram, angle QPR = 90o, angle PSR = 90o and PR = 5 units. Find the length of QS.
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A.
5 tan 25o sin 65o -
B.
5 cos 25o sin 65o -
C.
5 tan 25o cos 65o -
D.
cos 25o cos 65o -
E.
5 cosec 25o
Correct Answer: Option C
Explanation
From (bigtriangleup)QPR, o – (25o + 90o)
180o – 115o = 65o
From (bigtriangleup)PSQ, Sin 65o = (frac{QPR}{hyp}) = (frac{PS}{5})
PS = 5 sin 65o
From (bigtriangleup)PSR, tan = (frac{OPP}{adj}) = (frac{PS}{QS})
but PS = 5 sin 65o
QS tan 25o = PS
QS tan 25o = 5 sin 65o
QS = (frac{5 sin 65^o}{tan 25^o})
= 5 tan 25o cos 65o