In\( ∆ PQR, P\hat{Q}P = 84^°, |Q\hat{P}R |= 43^°\) and |PQ| = 5cm. Find /QR/ in cm, correct to 1 decimal place.
A
3.4
B
4.3
C
5.9
D
6.2
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Using the sine rule
\(\frac{|QR|}{sinP}=\frac{|PQ|}{sinR}\\
\frac{x}{sin43^o}=\frac{5}{sin53^o}\\
x = \frac{5\times sin43^o}{sin53^o}\\
=\frac{5\times 0.6820}{0.7986}\\
=4.3\)
Source: Myschool Past Questions Archive (Record #26587)