In (bigtriangleup)PQR, PQ = 10cm, QR = 8cm and RP = 6cm, the perpendicular RS is drawn from R to PQ. Find the length of RS

A.
4cm 
B.
32cm 
C.
(frac{30}{7}) 
D.
(frac{40}{7}) 
E.
4.8cm
Correct Answer: Option E
Explanation
Cos Q = (frac{r^2 + p^2 – q^2}{2rp})
= (frac{10^2 + 8^2 – 6^2}{2(10)(8)})
= (frac{164 – 36}{160})
= (frac{128}{160})
= 0.8
Q = Cos^{1} o.8
= 37^{o} x rep. from rt
(frac{x}{sin 37^o}) = (frac{8}{sin 90^o})
but sin 90^{o} = 1
x = 8 sin 37^{o}
x = 4.8cm