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Sholpan [36]
3 years ago
12

Find the length of the hypotenuse....

Mathematics
1 answer:
nika2105 [10]3 years ago
4 0

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.

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