Find the value of each variable. Write answer in simplest radical form.

Question

Aright triangle with 45° angles. X and Y are congruent and the hypotenuse is 10.

Answer 1

In this problem if you build a triangle with the adjacent side X and the opposite side Y with 45° in each side

!45º hypotenuse =10

!

Y

!

!_____________45º

X

sin45 = opposite/hypotense =. Y/10

√2/2 = Y/10 y= 10 x √2/2 =5√2

Now using the definition of cosine = adjacent /hypotenuse = X/10

cos45° = X/10. , therefore X= 10 x. √2/2= 5√2

Note: The reason that X and Y are equal is because the sine and cosine of 45º is the same .

Answer 2

Hi Alex G., this is an isosceles right triangle.

So x = y, 45^o = π/4, sin(θ) = side opposite / hypotenuse,

sin(π/4) = y/10

10*sin(π/4) = y

10*√2 / 2 = y

5*√2 = y = x

I hope this helps, Joe.