Question

Find the length of the hypotenuse....

Answer 1

Answer:

The length of the hypotenuse is 6 units.

∵ Option D is correct.

Step-by-step explanation:

Given

• The angle Ф = 45°

• The opposite side of angle Ф is $3\sqrt{2}$

To determine

The hypotenuse = ?

Using the trigonometric ratio

$sin\:\theta \:\:=\:\:\frac{opposite\:}{hypotenuse}$

In our case,

• Ф = 45°

• The opposite side of the Ф is $3\sqrt{2}$

now substituting Ф = 45° and opposite = $3\sqrt{2}$ in the trigonometric ratio formula

$\sin \left(45^{\circ \:\:}\right)=\:\:\frac{3\sqrt{2}\:}{hypotenuse}$

$\frac{\sqrt{2}}{2}=\frac{3\sqrt{2}\:}{hypotenuse}\:\:\:$            ∵ $\sin \left(45^{\circ \:}\right)=\frac{\sqrt{2}}{2}$

$hypotenuse\:=\frac{2\times 3\sqrt{2}}{\sqrt{2}}$

$\:hypotenuse\:=\frac{6\sqrt{2}}{\sqrt{2}}$

$hypotenuse\:=\:6$ units

Therefore, the length of the hypotenuse is 6 units.

∵ Option D is correct.