Shape and Space 10

4 marks · Hard

In triangle DEF, side DE = 11.3 cm, side EF = 8.7 cm, and angle DEF = 38°. Calculate the length of side DF. Give your answer correct to 3 significant figures.

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7.17 cm (to 3 s.f.) cm (±0.01)

Also accept: 7.18 cm

Common mistakes: Omitting the square root; Incorrect formula: using sine rule or area rule

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Appropriate use of the cosine rule with correct formula substitution

M2 · 1 mark · Correctly substitute the side lengths and angle into the formula

A1 · 1 mark · Accurate evaluation of the arithmetic, leading up to the value before square rooting

A2 · 1 mark · Final answer for DF correct to 3 significant figures

Worked solution

We are given DE, EF, and included angle DEF. Use the cosine rule:

Substitute values:

Rounding to three significant figures: .