The diagram shows a cuboid $ABCDEFGH$.
$AB = 8$ cm, $BC = 6$ cm and $CG = 5$ cm.
(a) Work out the length of $AG$. Give your answer correct to 3 significant figures. [3]
(b) Work out the size of the angle between $AG$ and the plane $ABCD$. Give your answer correct to 1 decimal place. [3]
- (a) for $AC^2 = 8^2 + 6^2$ or $AC = 10$M1
- for $AG = \sqrt{10^2 + 5^2}$ or $\sqrt{8^2 + 6^2 + 5^2}$M1
- $11.2$ (cm) (accept $11.18\ldots$)A1
- (b) for identifying angle $GAC$ as the required angle (may be implied by working)M1
- for $\tan^{-1}\left(\dfrac{5}{10}\right)$ or $\sin^{-1}\left(\dfrac{5}{\sqrt{125}}\right)$ or $\cos^{-1}\left(\dfrac{10}{\sqrt{125}}\right)$ oeM1
- $26.6^\circ$ (accept $26.56\ldots$)A1
- Answer: (a) 11.2 cm (b) 26.6°
- Examiner tip: The angle with a plane is between the line and its projection on the plane — here AC, not AB.