PR2=PQ2+RQ2−2(PQ)(RQ)cosQPR^2 = PQ^2 + RQ^2 - 2(PQ)(RQ)\cos QPR2=PQ2+RQ2−2(PQ)(RQ)cosQ
→cosQ=PQ2+RQ2−PR22(PQ)(RQ)\rightarrow\cos Q = \frac{PQ^2 + RQ^2 - PR^2}{2(PQ)(RQ)}→cosQ=2(PQ)(RQ)PQ2+RQ2−PR2
→cosQ=82+52−722×8×5\rightarrow\cos Q = \frac{8^2 + 5^2 - 7^2}{2\times 8\times 5}→cosQ=2×8×582+52−72
→cosQ=64+25−4980\rightarrow\cos Q = \frac{64 + 25 - 49}{80}→cosQ=8064+25−49
→cosQ=4080=0.5\rightarrow\cos Q = \frac{40}{80} = 0.5→cosQ=8040=0.5
→Q=cos−1(0.5)=60∘\rightarrow Q = \cos^{-1} (0.5) = 60^{\circ}→Q=cos−1(0.5)=60∘
∴x=60∘\therefore x = 60^{\circ}∴x=60∘
