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(A) In a right-angled triangle,let the angles be $30^{\circ}$,$60^{\circ}$,and $90^{\circ}$.According to trigonometric ratios,for an angle $	heta$,$\

Vedclass · Accepted Answer

$\frac{1}{2}$

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(A) In a right-angled triangle,let the angles be $30^{\circ}$,$60^{\circ}$,and $90^{\circ}$.According to trigonometric ratios,for an angle $	heta$,$\sin(	heta) = \frac{	ext{opposite side}}{	ext{hypotenuse}}$.Here,$	heta = 30^{\circ}$.Therefore,$\sin(30^{\circ}) = \frac{	ext{side opposite to } 30^{\circ}}{	ext{hypotenuse}}$.We know that $\sin(30^{\circ}) = \frac{1}{2}$.Thus,$\frac{1}{2} = \frac{	ext{side opposite to } 30^{\circ}}{	ext{hypotenuse}}$.This implies that the side opposite to the $30^{\circ}$ angle is $\frac{1}{2}$ times the hypotenuse.

In a right triangle,if the measure of one of the angles is $30^{\circ}$,then the side opposite to the angle with measure $30^{\circ}$ is .......... times the hypotenuse.

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