Let ∆ABC be the right-angled triangle in which
![\[\angle B\text{ }=\text{ }{{90}^{o}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c9b2b22bc6477cdbe702ecb07e0ce152_l3.png "Rendered by QuickLaTeX.com")
Let
![\[\mathbf{AC}\text{ }=\text{ }\mathbf{x},\text{ }\mathbf{BC}\text{ }=\text{ }\mathbf{y}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ab512b4e4a8050f096e6f25bfdc37854_l3.png "Rendered by QuickLaTeX.com")
In this way,
![\[\mathbf{AB}\text{ }=\text{ }\surd \left( \mathbf{x2}\text{ }+\text{ }\mathbf{y2} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d0313249048a7060655dc19e2c685390_l3.png "Rendered by QuickLaTeX.com")
![\[\angle \mathbf{ACB}\text{ }=\text{ }\mathbf{\theta }\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-40a00755dde86ef8e7f8c07eb2bd9f78_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{Let}\text{ }\mathbf{z}\text{ }=\text{ }\mathbf{x}\text{ }+\text{ }\mathbf{y}\text{ }\left( \mathbf{given} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-639422a774486bb0aa4ae9e09eb44b3a_l3.png "Rendered by QuickLaTeX.com")
Presently, the space of
![\[\mathbf{ABC}\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ }\mathbf{x}\text{ }\mathbf{AB}\text{ }\mathbf{x}\text{ }\mathbf{BC}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-76a4d69f80aa485b2f34fae7c183bca6_l3.png "Rendered by QuickLaTeX.com")
Thusly, the space of the given triangle is greatest when the point between its hypotenuse and a side is π/3.
Let ∆ABC be the right-angled triangle in which
Let
In this way,
Presently, the space of
Thusly, the space of the given triangle is greatest when the point between its hypotenuse and a side is π/3.