Question

A $7$ m long flagstaff is fixed on the top of a tower standing on the horizontal plane. From point on the ground, the angles of elevation of the top and bottom of the flagstaff are ${60}^{\circ }$ and ${45}^{\circ }$ respectively. Find the height of the tower correct to one place of decimal. (Use $\sqrt{3}=1.73$)

Answer 1

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In $\Delta BCD:-tan{45}^{\circ }=\frac{BC}{CD}$

$\Rightarrow 1=\frac{h}{CD}\Rightarrow CD=h$

In $\Delta ACD:-tan{60}^{\circ }=\frac{h+7}{CD}$

$\sqrt{3}=\frac{h+7}{h}\Rightarrow (\sqrt{3}-1)h=7$

$h=\frac{7}{0.73}=9.6m$