Shape and Space 10

3 marks · Normal

In triangle PQR, cm, cm, and . Calculate the length of QR. Give your answer correct to 3 significant figures.

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

7.74 cm (±0.02)

Must show: Use sine rule correctly

Also accept: 7.75 cm

Common mistakes: Incorrect use of sine rule (wrong arrangement)

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Method: Sets up sine rule correctly with . (follow-through)

M2 · 1 mark · Method: Finds a required angle using 180° sum, or uses sine rule arrangement correctly for sides. (follow-through)

A1 · 1 mark · Accuracy: QR calculated correctly to 3 significant figures. (follow-through)

Worked solution

Let QR = x. In triangle PQR, using the sine rule:

First, calculate angle P:

Sum of angles = 180°, so , but since only sides and angle at P are known, we use the sine rule for QR:

But we don't know angle Q or angle R. However, the correct form sets as:

But again, both remaining angles are unknown. Instead, as both sides containing the included angle are given, use the cosine rule:

QR = 7.52 cm (3 significant figures)