Problem Statement
From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of a $20\text{ m}$ high building are $45^\circ$ and $60^\circ$ respectively. Find the height of the tower. (Take $\sqrt{3} = 1.732$)
Verified Solution & Marking Scheme
Find Distance from Ground Point
$\tan 45^\circ = \frac{20}{x} \implies x = 20\text{ m}$.
Find Tower Height
$\tan 60^\circ = \frac{20 + h}{20} \implies 20\sqrt{3} = 20 + h \implies h = 20(\sqrt{3} - 1)$.
Evaluate Decimal
$h = 20(1.732 - 1) = 20(0.732) = 14.64\text{ m}$