IB Mathematics Analysis and Approaches Question Type 4: Using Cosine Rule to Find the 3rd Side Exercises

Triangle GHI has $g=10$, $h=14$ and angle $I=30^{\circ }$. Find the length of side $i$.

Calculate side $f$.

In triangle ABC, sides $a=6$, $b=8$ and included angle $C=65^{\circ }$. Find the length of side $c$.

Triangle EFG has $e=25$, $f=30$ and $G=150^{\circ }$. Find $g$.

In triangle HIJ, $h=100$, $i=120$ and $J=5^{\circ }$. Determine side $j$.

Triangle $YZA$ has $y=13.5$, $z=9.8$ and angle $A=110^{\circ }$. Find side $a$.

Triangle $MNO$ has sides $m=4.5$, $n=7.2$ and angle $O=45^{\circ }$. Find $o$.

Triangle STU has equal sides $s=t=8$ and angle $U=36^{\circ }$. Find side $u$.

In triangle BCD, $b=50$, $c=60$ and angle $D=25^{\circ }$. Calculate $d$.

In triangle $VWX$, $v=11$, $w=17$ and angle $X=92^{\circ }$. Determine $x$.

In triangle JKL, $j=9$, $k=12$ and angle $L=120^{\circ }$. Determine $l$.

In triangle PQR, $p=15$, $q=20$ and angle $R=75^{\circ }$. Calculate $r$.