Question 13
In triangle $$PQR$$, $$\angle R=2\angle P$$, $$PR=5$$ and $$QR=4$$. The length of $$PQ$$ is
Solution
Let $$PQ=x$$ and $$\angle P=\theta$$. The sine rule gives $$\frac{x}{\sin2\theta}=\frac{4}{\sin\theta}$$, so $$x=8\cos\theta$$. Applying the cosine rule at $$P$$ gives $$16=25+x^2-10x\cos\theta=25-\frac{x^2}{4}$$, and hence $$x=6$$.
Get AI Help
Book Free CAT Mentorship
Get personalized CAT strategy from a 99%iler
500+ students mentored
OTP Verification
Enter the 6-digit code sent to your phone
Booking Summary
Session:Free CAT Mentorship
Phone:
Date:
Time:
Enter OTP
Didn't receive the OTP?
