iGCSE Mathematics (0580) :E6.2 Apply Pythagoras’ theorem.iGCSE Style Questions Paper 2

Question

Calculate the length $ BC $.

▶️ Answer/Explanation

Solution

Ans: 12.7 cm (12.68 to 12.69)

1. Find angle C: $ 180 – 115 – 35 = 30° $

2. Apply sine rule: $ \frac{BC}{\sin 115} = \frac{7}{\sin 30} $

3. Calculate: $ BC = \frac{7 \times \sin 115}{\sin 30} $

4. Evaluate: $ \sin 115 ≈ 0.9063 $, $ \sin 30 = 0.5 $

5. Final calculation: $ BC ≈ 12.688 $ cm

Question

Calculate the obtuse angle $PRQ$.

▶️ Answer/Explanation

Solution

Ans: 116.9°

1. Use sine rule: $\frac{QR}{\sin P} = \frac{PQ}{\sin R}$

2. $\sin R = \frac{PQ \sin P}{QR} = \frac{13.5 \sin 42°}{18}$ ≈ 0.5

3. Acute angle would be ≈63.1°

4. Obtuse angle = 180° – 63.1° = 116.9°

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