Question

If the legs of an isosceles right triangle have a length of 15√2 ft, the hypotenuse will have a length of _____feet.

Answer 1

Answer:

The hypotenuse will have a length of __30___feet.

Step-by-step explanation:

An isosceles right triangle:

It is a right triangle with two legs equal in length and has angles of  $45^{\circ}-45^{\circ}-90^{\circ}$

In a  $45^{\circ}-45^{\circ}-90^{\circ}$ triangle,

the length of the hypotenuse is $\sqrt{2}$ times the length of a leg.

Given the statement:

If the legs of an isosceles right triangle have a length of 15√2 ft.

⇒Length of leg = 5√2 ft

then by definition we have;

$\text{Length of hypotenuse} = \sqrt{2} \cdot 15\sqrt{2}$

Simplify:

$\text{Length of hypotenuse} = 15 \cdot 2 = 30 ft$

Therefore, the hypotenuse will have a length of __30___feet.

Answer 2

we know that

An isosceles triangle has two equal sides and two equal angles

If the isosceles triangle is a right triangle

then

The measure of the angles are  $45\°- 90\°- 45\°$

$cos (45\°)=\frac{\sqrt{2}}{2}$

$cos (45\°)=\frac{leg}{hypotenuse}$

so

$\frac{leg}{hypotenuse}=\frac{\sqrt{2}}{2}$

we have

$leg=15\sqrt{2}\ ft$

Substitute and solve for the hypotenuse

$\frac{15\sqrt{2}}{hypotenuse}=\frac{\sqrt{2}}{2}\\ \\hypotenuse=2*15 \\ \\ hypotenuse=30\ ft$

therefore

the answer is

$30\ feet$