If two towers of height h1 …
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Sia ? 6 years, 4 months ago
Let{tex} AB\ and \ CD{/tex} are towers of height {tex} h_1 \ and \ h_2{/tex} respectively.
If E is the midpoint of BD then {tex}BE = DE = x{/tex}
In right {tex}\triangle{/tex}ABE
{tex}\frac { h _ { 1 } } { x }{/tex}{tex} = tan 60° {/tex}
{tex}\Rightarrow{/tex} h1 = {tex}\sqrt { 3 } x{/tex}
In right {tex}\triangle{/tex}CDE {tex}\frac { h _ { 2 } } { x }{/tex}= tan 30° {tex}\Rightarrow h _ { 2 } = \frac { x } { \sqrt { 3 } }{/tex}
Now {tex}\frac { h _ { 1 } } { h _ { 2 } } = \frac { \sqrt { 3 } x } { \frac { x } { \sqrt { 3 } } } = \frac { 3 } { 1 }{/tex} {tex}\Rightarrow h _ { 1 } : h _ { 2 } = 3 : 1{/tex}
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