Use the information given to find the length of AB.

In Δ APQ,

$\text{tan 30°} = \dfrac{Perpendicular}{Base}\\[1em] ⇒ \dfrac{1}{\sqrt3} = \dfrac{AQ}{AP}\\[1em] ⇒ \dfrac{1}{\sqrt3} = \dfrac{10}{AP}\\[1em] ⇒ AP = 10 \sqrt3 = 17.32 cm$

In Δ PBR,

$\text{tan 45°} = \dfrac{Perpendicular}{Base}\\[1em] ⇒ 1 = \dfrac{PB}{BR}\\[1em] ⇒ 1 = \dfrac{PB}{8}\\[1em] ⇒ PB = 8 cm$

AB = AP + PB

= 17.32 + 8 cm

= 25.32 cm

Hence, AB = 25.32 cm.