The angle of elevation of the top of a hill from a point on the...

$x = 80\cos 30 ° = 40\sqrt{3}$

$y = 80\sin 30 ° = 40$

$\tan 45 ° = 1$

$⇒ x + z = h$

$⇒ 40\sqrt{3} + z = h$

$\tan 75 ° = \dfrac{h - y}{z}$

$⇒ 2 + \sqrt{3} = \dfrac{h - 40}{z}$

$⇒ z = \dfrac{h - 40}{2 + \sqrt{3}}$

$⇒ h - 40\sqrt{3} = \dfrac{h - 40}{2 + \sqrt{3}}$

$( 1 + \sqrt{3} ) h = 80 ( 1 + \sqrt{3} )$

$h = 80$