iGCSE Mathematics (0580) : C6.2 Apply Pythagoras’ theorem and the sine, cosine and tangent ratios iGCSE Style Questions Paper 1

Question

The diagram shows a right-angled triangle ABC.
AC = 15 cm and angle BAC = 38°.

Calculate BC.

▶️ Answer/Explanation

Solution

Ans: 9.23 cm

Use sine ratio: sin(38°) = opposite/hypotenuse = BC/15

Rearrange: BC = 15 × sin(38°)

Calculate: 15 × 0.6157 ≈ 9.2355 cm

Rounded to 3 significant figures: 9.23 cm

Question

The diagram shows a right-angled triangle.

Show that the value of x is 15.8, correct to 3 significant figures.

▶️ Answer/Explanation

Solution

Ans: 15.8 cm

Using tangent function: tan(48°) = opposite/adjacent = x/17.5

Therefore, x = 17.5 × tan(48°) ≈ 17.5 × 1.1106 ≈ 19.435

Alternatively, tan(42°) = 17.5/x → x ≈ 17.5/0.9004 ≈ 19.435

Rounding to 3 significant figures gives x ≈ 19.4 cm

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