Labelling. In triangle ABC, which side is side \(a\)?

1. The side joining B and C
2. The side joining A and B
3. The side joining A and C
4. The longest side

Answer: The side joining B and C

Side \(a\) is the side OPPOSITE angle A.

Angle A sits at vertex A, so the side across from it joins the other two vertices, B and C.

Tip: Side \(a\) never touches angle A. Look ACROSS the triangle.

Labelling. In any triangle, \(\hat{A} + \hat{B} + \hat{C}\) equals:

1. \(180^\circ\)
2. \(360^\circ\)
3. \(90^\circ\)
4. It depends on the triangle

Answer: \(180^\circ\)

The three interior angles of any triangle always add to \(180^\circ\).

Tip: This is often the missing first step that creates a complete angle-side pair.

Labelling. In a triangle, the largest angle is always found:

1. opposite the longest side
2. opposite the shortest side
3. between the two longest sides
4. at vertex A

Answer: opposite the longest side

Bigger angles "open up" wider, so the side stretching across them is longer.

Tip: A quick sanity check on any answer you calculate.

Area rule. Which formula is the area rule?

1. \(\text{Area} = \tfrac{1}{2}ab\sin C\)
2. \(\text{Area} = \tfrac{1}{2}ab\cos C\)
3. \(\text{Area} = ab\sin C\)
4. \(\text{Area} = \tfrac{1}{2}ab\tan C\)

Answer: \(\text{Area} = \tfrac{1}{2}ab\sin C\)

The area rule comes from \(\text{Area}=\tfrac12\times\text{base}\times\text{height}\), where the height is \(b\sin A\).

Tip: Sine, not cosine - and remember the half.

Area rule. In triangle ABC, \(b = 7\) cm, \(c = 9\) cm and \(\hat{A} = 50^\circ\). Calculate the area.

1. \(24{,}13\text{ cm}^2\)
2. \(48{,}26\text{ cm}^2\)
3. \(20{,}25\text{ cm}^2\)
4. \(31{,}50\text{ cm}^2\)

Answer: \(24{,}13\text{ cm}^2\)

A sits between sides \(b\) and \(c\), so the area rule applies directly.

\(\text{Area} = \tfrac{1}{2}bc\sin A = \tfrac{1}{2}(7)(9)\sin 50^\circ\)

Tip: \(31{,}50\) is what you get if you forget the \(\sin 50^\circ\).