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(D) Let the right triangle be $	riangle ABC$,where $\angle B = 90^{\circ}$ and $\angle C = 45^{\circ}$.In $	riangle ABC$,the side opposite to $\angl

Vedclass · Accepted Answer

$\frac{1}{\sqrt{2}}$

Vedclass · Answer

(D) Let the right triangle be $	riangle ABC$,where $\angle B = 90^{\circ}$ and $\angle C = 45^{\circ}$.In $	riangle ABC$,the side opposite to $\angle C$ is $AB$ and the hypotenuse is $AC$.Using the trigonometric ratio $\sin 	heta = \frac{	ext{opposite side}}{	ext{hypotenuse}}$:$\sin 45^{\circ} = \frac{AB}{AC}$Since $\sin 45^{\circ} = \frac{1}{\sqrt{2}}$,we have:$\frac{1}{\sqrt{2}} = \frac{AB}{AC}$Therefore,$AB = \frac{1}{\sqrt{2}} AC$.Thus,the measure of the side opposite to the angle of $45^{\circ}$ is $\frac{1}{\sqrt{2}}$ times the measure of the hypotenuse.

In a right triangle,if the measure of one of the angles is $45^{\circ}$,then the measure of the side opposite to the angle with measure $45^{\circ}$ is $\ldots \ldots \ldots$ times the measure of the hypotenuse.

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