Question

Match the height of the tower (h) in each case.

• A. $20\sqrt{3}$ m
• B. 12 m
• C. $10\sqrt{3}$ m

Answer 1

tan 60 = $\frac{h}{20}$

$\sqrt{3}$ = $\frac{h}{20}$

h = 20$\sqrt{3}$ m

For 2nd figure,

$tan30=\frac{h}{30}$

$\frac{1}{\sqrt{3}}=\frac{h}{30}$

$h=\frac{30}{\sqrt{3}}$

$h=10\sqrt{3}m$

For 3rd figure,

$tan\alpha =\frac{h}{9}.........\left(i\right)$

$tan(90-\alpha )=\frac{h}{16}$

$cot\alpha =\frac{h}{16}$

$tan\alpha =\frac{16}{h}.......\left(ii\right)$

equating equations ( i ) and ( ii ) we get ,

$\frac{h}{9}=\frac{16}{h}$

$h^2=3^2\times 4^2$

$\therefore h=12m$