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
Verified Correct Answer: E.
Step-by-Step Mathematical Solution
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
= 37o x rep. from rto = 1
x = 8 sin 37o
x = 4.8cm
Source: Myschool Past Questions Archive (Record #32648)