IB Mathematics Analysis and Approaches Question Type 5: Using Cosine Rule to Find All the Angles Between Sides Exercises

Points $A(1,2)$, $B(7,5)$, and $C(-2,9)$ form a triangle. Find $\angle A$, $\angle B$, and $\angle C$ to $1$ decimal place.

A triangle has side lengths $6.2\text{ cm}$, $8.5\text{ cm}$, and $10.3\text{ cm}$. Find all three angles to $1$ decimal place.

Given a triangle with side lengths $11.7\text{ cm}$, $18.2\text{ cm}$, and $24.6\text{ cm}$, find all angles to $1$ decimal place.

Two sides of a triangular field are $35\text{ m}$ and $48\text{ m}$, and the included angle is $73^{\circ }$. Find the remaining two angles to $1$ decimal place.

Two sides of a triangle are $AB=9\text{ cm}$ and $AC=10\text{ cm}$, with included angle $\angle A=120^{\circ }$. Find the remaining two angles to $1$ decimal place.

A triangle has sides $20\text{ cm}$, $21\text{ cm}$, and $29\text{ cm}$. Find all three interior angles to $1$ decimal place.

The sides of a triangular park are $AB=23\text{ km}$, $BC=17\text{ km}$, and $CA=19\text{ km}$. Find all three interior angles to $1$ decimal place.

An isosceles triangle has side lengths $9\text{ cm}$, $9\text{ cm}$, and $14\text{ cm}$. Find all interior angles to $1$ decimal place.

Find all angles of a triangle with side lengths $5\text{ cm}$, $6\text{ cm}$, and $7\text{ cm}$, to $1$ decimal place.

Consider a triangle with sides $a=7\text{ cm}$, $b=8\text{ cm}$, and $c=5\text{ cm}$. Find all three interior angles to $1$ decimal place.

In $△ABC$, $AB=12\text{ cm}$, $AC=8\text{ cm}$, and $\angle A=40^{\circ }$. Find $\angle B$ and $\angle C$ to $1$ decimal place.

In $△ABC$, the sides are $a=9\text{ cm}$, $b=10\text{ cm}$, and $c=11\text{ cm}$. Find all angles to $1$ decimal place.

In $△ABC$, the side lengths are $a=13$, $b=14$, $c=15$. Find $\angle A$, $\angle B$, and $\angle C$ to $1$ decimal place.