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

`5.2\ units`

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\°)=(x)/((26√(2)/5))`

`cos(45\°)=(√(2))/(2)`

so

`(√(2))/(2)=(x)/((26√(2)/5))\\ \\x=26/5\\ \\x=5.2\ units`