A cube has its vertices on the top face labeled $A$A, $B$B, $C$C, and $D$D in clockwise order, starting from the rear-left vertex. The vertices on the bottom face are labeled $E$E, $F$F, $G$G, and $H$H in clockwise order, also starting from the rear-left vertex.

Find the length of $EG$EG. Give your answer as a surd in simplest form.

Find the length of $AG$AG. Give your answer as a surd in simplest form.

Find $x$x, the size of $\angle EGH$∠EGH.

Find $y$y, the size of $\angle EGA$∠EGA, correct to two decimal places.

Find $w$w, the size of $\angle AHG$∠AHG.

Find $z$z, the size of $\angle AGH$∠AGH, correct to two decimal places.

Easy

13 min

A square prism has sides of length $7$7cm, $7$7cm and $17$17cm as shown.

Easy

4 min

This box is to have a divider placed in as shown.

Easy

2 min

The diagram shows a rectangular prism.

Easy

2 min

Outcomes

0580E6.5

Solve simple trigonometrical problems in three dimensions including angle between a line and a plane.

20.08 Trigonometry in 3D (Extended)

Interactive practice questions

Outcomes

0580E6.5

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