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 [tex]45\°- 90\°- 45\°[/tex]
[tex]cos (45\°)=\frac{\sqrt{2}}{2}[/tex]
[tex]cos (45\°)=\frac{leg}{hypotenuse}[/tex]
so
[tex]\frac{leg}{hypotenuse}=\frac{\sqrt{2}}{2}[/tex]
we have
[tex]leg=15\sqrt{2}\ ft[/tex]
Substitute and solve for the hypotenuse
[tex]\frac{15\sqrt{2}}{hypotenuse}=\frac{\sqrt{2}}{2}\\ \\hypotenuse=2*15 \\ \\ hypotenuse=30\ ft[/tex]
therefore
the answer is
[tex]30\ feet[/tex]
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 [tex]45^{\circ}-45^{\circ}-90^{\circ}[/tex]
In a [tex]45^{\circ}-45^{\circ}-90^{\circ}[/tex] triangle,
the length of the hypotenuse is [tex]\sqrt{2}[/tex] 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;
[tex]\text{Length of hypotenuse} = \sqrt{2} \cdot 15\sqrt{2}[/tex]
Simplify:
[tex]\text{Length of hypotenuse} = 15 \cdot 2 = 30 ft[/tex]
Therefore, the hypotenuse will have a length of __30___feet.
