Question

(c) Figure 6 shows the triangle ABC, with all side lengths measured in centimetres.

side AB = 14.6 cm
side AC = 21.4 cm
side BC = 7.5 cm
(i) Find angle ABC, giving your answer correct to the nearest degree.
(ii) Find the area of triangle ABC, giving your answer correct to the nearest square centimetre.​

Answer 1

• angle B ≈ 149°
• area ≈ 28 cm²

Explanation:

You want the largest angle and the area of a triangle with side lengths 7.5 cm, 14.6 cm, and 21.4 cm.

Law of cosines

The law of cosines tells you ...

b² = a² + c² -2ac·cos(B)

Solving for angle B, we have ...

B = arccos((a² +c² -b²)/(2ac))

B = arccos((7.5² +14.6² -21.4²)/(2·7.5·14.6)) ≈ 149° . . . angle ABC

Area

The area of the triangle can be found using the formula ...

Area = 1/2(ac·sin(B))

Area = 1/2·7.5·14.6·sin(149°) ≈ 28 cm² . . . area

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Additional comment

Angle ABC is opposite side AC, which is the longest side. Hence, angle ABC is the largest angle.

We used the original (full precision) angle value to calculate the area. The rounded angle value would be inappropriate for that purpose. (Second attachment.) Note the calculator mode is set to DEGrees.