Find PQ, if AB = 150 m, ∠P = 30° and ∠Q = 45°

In Δ APB,

$\text{tan 30°} = \dfrac{Perpendicular}{Base}\\[1em] ⇒ \dfrac{1}{\sqrt3} = \dfrac{AB}{PB}\\[1em] ⇒ \dfrac{1}{\sqrt3} = \dfrac{150}{PB}\\[1em] ⇒ PB = 150\sqrt3 = 259.80$

And, in Δ ABQ,

$\text{tan 45°} = \dfrac{Perpendicular}{Base}\\[1em] ⇒ 1 = \dfrac{AB}{BQ}\\[1em] ⇒ 1 = \dfrac{150}{BQ}\\[1em] ⇒ BQ = 150$

As, PQ = PB - BQ

= 259.80 - 150 m

= 109.80 m

Hence, PQ = 109.80 m.