Question

Suppose you have a right triangle with congruent legs and a hypotenuse that measure 26 square-root of 2 divided by 5. What is the length of one of the legs? Round to the nearest tenth.

Answer 1

Answer:

$5.2\ units$

Step-by-step explanation:

Let

x-----> the length of the congruent legs

we know that

If the triangle is a right triangle with congruent legs

then

the measures of the internal angles are 45°-90°-45°

therefore

$cos(45\°)=\frac{x}{(26\sqrt{2}/5)}$

$cos(45\°)=\frac{\sqrt{2}}{2}$

so

$\frac{\sqrt{2}}{2}=\frac{x}{(26\sqrt{2}/5)}\\ \\x=26/5\\ \\x=5.2\ units$