Question

The hypotenuse of a 45°-45°-90° triangle measures 22 2 units.

Answer 1

Answer:

Option C.

Step-by-step explanation:

Given information: The hypotenuse of a 45°-45°-90° triangle measures 22√2 units.

Let x be the length of one leg.

From the given figure it is clear that length of both legs are same.

According to the Pythagoras theorem, in a right angled triangle

$(leg_1)^2+(leg_2)^2=hypotenuse^2$

Substitute $leg_1=leg_2=x, hypotenuse=22\sqrt{2}$ in the above formula.

$(x)^2+(x)^2=(22\sqrt{2})^2$

$2x^2=(22)^2(\sqrt{2})^2$

$2x^2=2(22)^2$

Divide both sides by 2.

$x^2=(22)^2$

Taking square root on both sides.

$x=22$

The length of one leg is 22 units.

Therefore, the correct option is C.

Answer 2

Answer:

Length of one leg of the triangle be $22 \sqrt{2}$ .

Step-by-step explanation:

Now by using the trignometric property .

$sin \theta = \frac{Perpendicular}{Hypotenuse}$

As

$\theta = 90^{\circ}$

$Hypotenuse =22 \sqrt{2}$

Putting the values in the trignometric identity .

$sin90^{\circ} = \frac{Perpendicular}{22 \sqrt{2}}$

As sin 90° = 1

Put in the above

$1= \frac{Perpendicular}{22 \sqrt{2}}$

Thus

$Perpendicular = 22 \sqrt{2}$

Therefore the length of one leg of the triangle be $22 \sqrt{2}$ .