Answer:
The length of the hypotenuse is 6 units.
∵ Option D is correct.
Step-by-step explanation:
Given
- The opposite side of angle Ф is [tex]3\sqrt{2}[/tex]
To determine
The hypotenuse = ?
Using the trigonometric ratio
[tex]sin\:\theta \:\:=\:\:\frac{opposite\:}{hypotenuse}[/tex]
In our case,
- The opposite side of the Ф is [tex]3\sqrt{2}[/tex]
now substituting Ф = 45° and opposite = [tex]3\sqrt{2}[/tex] in the trigonometric ratio formula
[tex]\sin \left(45^{\circ \:\:}\right)=\:\:\frac{3\sqrt{2}\:}{hypotenuse}[/tex]
[tex]\frac{\sqrt{2}}{2}=\frac{3\sqrt{2}\:}{hypotenuse}\:\:\:[/tex] ∵ [tex]\sin \left(45^{\circ \:}\right)=\frac{\sqrt{2}}{2}[/tex]
[tex]hypotenuse\:=\frac{2\times 3\sqrt{2}}{\sqrt{2}}[/tex]
[tex]\:hypotenuse\:=\frac{6\sqrt{2}}{\sqrt{2}}[/tex]
[tex]hypotenuse\:=\:6[/tex] units
Therefore, the length of the hypotenuse is 6 units.
∵ Option D is correct.
