Question

lf the angle of elevation of the top of a tower from a point is ${60}^o$ and 40 metres vertically above this point the angle of elevation is ${45}^o$ The height of the tower in metres is

• A. $64.64$
• B. $94.64$
• C. $54.64$
• D. $74.64$

Answer 1

The correct option is B $94.64$

$\tan 45=\frac{h_1}{d}$

$1=\frac{h_1}{d}$ $⟹$ $h_1=d$

$\tan 60=\frac{40+h_1}{d}$

$\sqrt{3}=\frac{40+h_1}{d}$

$\sqrt{3}=\frac{h_1+40}{h_1}$

$h_1+40=\sqrt{3}{h}_1$

$h_1=\frac{40}{\sqrt{3}-1}$

Total height=$H=40+h_1=40+54.64=94.64$