IB Mathematics Applications & Interpretation Question Type 3: Finding Sides and Angles Using Sine Rule Exercises

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

In triangle $ABC$, $a=7$, $c=9$, and $A=40^{\circ }$. Find the possible values of angle $C$.

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

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

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

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