Introduction to the Cosine Rule

Flashcards covering the cosine rule formulas, algebraic rearrangements, step-by-step example calculations, and rules for choosing between the sine and cosine rules.

The standard formula for the cosine rule is __________.

$$a^2 = b^2 + c^2 - 2bc \cos(A)$$

When using the cosine rule to find a missing side $x$, that side should be labeled as __________.

$$a$$

In the first example with sides $11\,cm$ and $15\,cm$ and an included angle of $75^\circ$, the missing side length $x$ rounded to one decimal place is __________.

$$16.1\,cm$$

In the second example with sides $9\,cm$ and $6\,cm$ and an included angle of $62^\circ$, the missing side length $x$ rounded to one decimal place is __________.

$$8.1\,cm$$

The rearranged formula for the cosine rule used to find a missing angle is __________.

$$\cos(A) = \frac{b^2 + c^2 - a^2}{2bc}$$

To rearrange $a^2 = b^2 + c^2 - 2bc \cos(A)$ to find an angle, the first step is to add __________ to both sides.

$$2bc \cos(A)$$

After adding $2bc \cos(A)$ to both sides, the second step in rearranging the cosine rule for an angle is to subtract __________ from both sides.

$$a^2$$

When finding an angle using the rearranged cosine rule, the angle being calculated must be labeled as __________.

$$A$$

In the triangle with sides $7\,cm$, $5\,cm$, and opposite side $4\,cm$, the missing angle $x$ rounded to one decimal place is __________.

$$34.0^\circ$$

In the triangle with sides $15$, $9$, and opposite side $20$, the missing angle $x$ rounded to one decimal place is __________.

$$110.4^\circ$$

The cosine rule is used to find a missing side when you are given two sides and the angle __________.

in between those two sides

The cosine rule is used to find an angle when you are given __________ of the sides.

all three

You can identify that a question requires the sine rule when the given information involves __________ pairs of opposite side and angle values.

two