Melaka Trial 2025 Add Maths Paper 2, Question 12Solution of Triangles

Solved on video in English · Form 4, Solution of Triangles · 6:13 video

The question

(a)(i)

Diagram 6 shows a cyclic quadrilateral PQRS. It is given that ∠PQR = 85°, QR = 7.5 cm, PQ = 9 cm and RS = 4 cm.

(a) Calculate (i) the length, in cm, of PR.

(a)(ii)

Diagram 6 shows a cyclic quadrilateral PQRS with ∠PQR = 85°, QR = 7.5 cm, PQ = 9 cm, RS = 4 cm and PR = 11.20 cm.

(a)(ii) Calculate ∠PRS.

(b)(i)

Diagram 6 shows a cyclic quadrilateral PQRS with ∠PQR = 85°, QR = 7.5 cm, PQ = 9 cm and PR = 11.20 cm.

(b) Find (i) the area, in cm², of triangle PQR.

(b)(ii)

Diagram 6 shows a cyclic quadrilateral PQRS; triangle PQR has area 33.62 cm² and PR = 11.20 cm.

(b)(ii) Find the shortest distance, in cm, from point Q to PR.

Melaka Trial 2025 Add Maths Paper 2, Question 12: the question as drawn in Eduly's video6:13

Part (a)(i)

Step 1

In triangle PQR use the cosine rule with the included angle at Q.

Why this step

We know two sides and the angle between them, with no side and opposite angle pair, so the cosine rule is the one to use, not the sine rule.

3 more steps, each with the reason for it, in the full solution

Final answer

PR = 11.20 cm

Where students lose marks

Watch out: use the two sides around the 85° angle, keep the −2(QR)(PQ)cos term, and set your calculator to degree mode.

Part (a)(ii)

4 more steps, each with the reason for it, in the full solution

Final answer

∠PRS = 64.16°

Where students lose marks

Watch out: opposite angles of a cyclic quadrilateral add to 180°, so ∠PSR = 95°. Then pair each side with its opposite angle.

Part (b)(i)

3 more steps, each with the reason for it, in the full solution

Final answer

Area = 33.62 cm²

Where students lose marks

Watch out: use the two sides that enclose the 85° angle, QR and PQ, not PR. Set your calculator to degree mode for sin 85°.

Part (b)(ii)

3 more steps, each with the reason for it, in the full solution

Final answer

t = 6.004 cm

Where students lose marks

Watch out: the height to PR pairs with base PR, not QR or PQ. Keep the ½, or your height comes out halved.

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