Find the value of each variable. Write in radical form

Question

a right triangle with a 45 degree angle and a hypotenuse of 13 square root of 2. Both legs are the missing variables 

Answer 1

In a 45-45-90 right triangle the relationship is as follows:

x, x, x√2 for the legs and the hypotenuse respectively

if the hypotenuse is 13√2, then the legs are 13 and 13

check:

using the Pythagorean Theorem...

(13√2)^2=x^2+x^2

169*2=2x^2

169=x^2

x=13 again

Answer 2

Special right triangles have formulas to follow...

For a 45 - 45 - 90 degree triangle the formula is x - x - x√2

 

This example fits directly into the formula..

The hypotenuse of 13√2 is the x√2...

so it follows that "x" is 13.

 

And because the other two sides of the triangle are "x,"

their sides are each 13.

 

So, it follows the rule...

x - x - x√2

13 - 13 - 13√2

 

 

Sorry for the typo...fixed now