Home / CIE iGCSE Maths E6.6 Pythagoras’ theorem and trigonometry in 3D Exam Style Practice Questions- Paper 2

CIE iGCSE Maths E6.6 Pythagoras’ theorem and trigonometry in 3D Exam Style Practice Questions- Paper 2

CIE iGCSE Maths E6.6 Pythagoras’ theorem and trigonometry in 3D Exam Style Practice Questions- Paper 2

Question

$HD=4$cm$,EH=6.5$cm and $EF=9.1$ cm.

Calculate the angle between $CE$ and the base $CDHG.$

▶️Answer/Explanation

$33.2$ or $33.18…$

\( HD = 9.1 \text{ cm} \) (length of the base)
\( DC = 4 \text{ cm} \) (height)

Using the Pythagorean theorem
$
HC = \sqrt{HD^2 + DC^2}
$
$
HC = \sqrt{9.1^2 + 4^2}
$
$
= \sqrt{82.81 + 16}
$
$
= \sqrt{98.81}
$
$
HC \approx 9.94 \, \text{cm}
$
In triangle \( HGC \)
$
\tan(x) = \frac{ \text{height of the cuboid} }{ HC }
$
$
\tan(x) = \frac{6.5}{9.94}
$
$
\tan(x) \approx 0.654
$
$
x = \tan^{-1}(0.654)
$
$
x \approx 33.01^\circ
$

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