MYP Extended Mathematics 7.3 Cosine Rule Questionbank

If the cosine rule is written in the form ${\cos A = \frac{b^{2} + c^{2} - a^{2}}{2bc}}$, what is the resulting value of ${\cos A}$ if the triangle satisfies the condition ${a^{2} = b^{2} + c^{2}}$?

In triangle $DEF$, you are given $d = 10$, $e = 12$, and the included angle $\angle F = 45^{\circ}$. The length of side $f$ to two decimal places is $\underline{\qquad}$.

The side lengths $b$ and $c$ must be larger than $a$ for the cosine rule to work.

The value calculated for $\cos A$ was less than $-1$, and these side lengths cannot form a triangle.

The angle $A$ is exactly $180^{\circ}$ and the calculator cannot process it.

The calculator was in Radian mode instead of Degree mode.

14 km

9 km

16 km

12 km

$10\sqrt{2}$ km

20 km

10 km

$10\sqrt{3}$ km