In the diagram, angle QPR = 90o, angle PSR = 90o and PR = 5 units. Find the length of QS.
Attached Figure / Diagram
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
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #32758)