iGCSE Mathematics (0580) :E6.1 Interpret and use three-figure bearings.iGCSE Style Questions Paper 2

Question

Calculate the value of $x$.

▶️ Answer/Explanation

Solution

$x = 54.3°$

Use cosine ratio: $\cos x = \frac{7}{12}$

Calculate inverse cosine: $x = \cos^{-1}(\frac{7}{12})$

Evaluate: $x ≈ 54.31°$ (round to 54.3°)

Question

The diagram shows a cuboid ABCDEFGH.
AB = 14 cm, BC = 5 cm and CG = 8 cm.
M is the midpoint of HG.

(a) Calculate BM.

(b) Calculate the angle that BM makes with the base ABCD.

▶️ Answer/Explanation

Solution

(a) Ans: 11.7 cm

First find horizontal distance from B to M: 7 cm (half AB) and 5 cm (BC).

Then use 3D Pythagoras: √(7² + 5² + 8²) = √(49 + 25 + 64) = √138 ≈ 11.7 cm

(b) Ans: 43.0°

Angle is between BM and its projection on base. Vertical component is 8 cm.

tanθ = 8/√(7² + 5²) → θ = tan⁻¹(8/√74) ≈ 43.0°

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