SPM 2023 Add Maths Paper 2, Question 12Solution of Triangles

Solved on video in English and Bahasa Melayu · Form 4, Solution of Triangles · 9:07 video

The question

(a)(i)

(Solutions by scale drawing are not accepted.) Diagram 6 shows a model consisting of a vertical wall ABCD and a horizontal floor CDEF, where CDEF is a parallelogram. It is given that AB = 35 cm, AD = 4 cm, ∠DFE = 30° and ∠DFC = 80°.

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

(a)(ii)

Diagram 6: vertical wall ABCD with AB = 35 cm, AD = 4 cm; horizontal parallelogram floor CDEF; ∠DFE = 30°, ∠DFC = 80°; CF = 17.77 cm.

(a)(ii) Calculate the area, in cm², of triangle ACE.

(b)

From the model, AE = 18.21 cm.

(b) A pole of length 5 cm is placed obliquely at corner E. A stick is used to join the top of the pole, G, to corner A, such that ∠EAG = 15°. Find the minimum length, in cm, of the stick.

SPM 2023 Add Maths Paper 2, Question 12: the question as drawn in Eduly's video9:07

Part (a)(i)

Step 1

In parallelogram CDEF, DC ∥ EF, so ∠FDC = ∠DFE = 30° (alternate angles). Also DC = AB = 35 cm.

Why this step

Parallel sides make alternate angles equal, so the 30° at F is also at D. We need it because it faces CF, the side we want.

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

Final answer

CF = 17.77 cm

Where students lose marks

Watch out: DC is opposite 80° and CF is opposite 30°. Putting the ratio the wrong way round gives a wrong CF.

Part (a)(ii)

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

Final answer

305.38 cm²

Where students lose marks

Watch out: ∠EAC is not 90°. Find it with the cosine rule first, or you get 320.77 cm² instead of 305.38 cm².

Part (b)

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

Final answer

AG = 15.93 cm

Where students lose marks

Watch out: sin ∠AGE = 0.9426 gives two angles, 70.54° and 109.46°. Taking only the acute one misses the shorter stick.

Watch every step of this question solved on video (9:07), with the reason behind each step and a box that checks your own answer.

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