Question Type 3: Finding sides and angles using sine rule Exercises

In triangle ABC, sides are $a=5$, $b=4$, and angle $A=30^\circ$. Find angle $B$ using the sine rule.

In triangle ABC, sides are $a=6$, $b=8$, and angle $B=65^\circ$. Find angle $A$ using the sine rule.

In triangle ABC, sides $a=10$, $b=7$, and included angle $C=50^\circ$. Find side $c$ using the cosine rule.

In triangle ABC, sides are $a=6$, $b=8$, with included angle $C=65^\circ$. Find the third side $c$ using the cosine rule.

In triangle ABC, $a=7$, $c=9$, and $A=40^\circ$. Find angle $C$ using the sine rule.

In triangle ABC, angles are $A=55^\circ$, $C=50^\circ$, and side $a=14$. Find side $c$ using the sine rule.

In the same triangle ($a=6$, $b=8$, $B=65^\circ$), find angle $C$ and side $c$.

In triangle ABC, angles are $A=45^\circ$, $B=75^\circ$, and side $a=8$. Find side $b$ using the sine rule.

For the triangle with $a=6$, $b=8$, and $C=65^\circ$, find the perimeter.

In the triangle with sides $9$, $18$, and $10$, find the largest interior angle.

Given a triangle with sides $a=9$, $b=18$, $c=10$, find angle $A$ using the cosine rule.

In the triangle with sides $9$, $18$, and $10$, find all interior angles.