\(\)Determine the value of a.
Draw WY to create △WXY .
△WXY is an isoscelese right triangle so the measure of each base angle is 45°
The length of each leg of △WXY is 4 so the length of the hypotenuse is 4√2
m∠XYZ = 135°
m∠WYZ = m∠XYZ - m∠WYX = 135° - 45º = 90°
So △WYZ is a right triangle, and we know the length of two of the sides.
To find the length of the missing side, we can use the Pythagorean theorem.
a2 + ( 4√2 )2 = 92
a2 + 32 = 81
Subtract 32 from both sides.
a2 = 49
Take the positive sqrt of both sides.
a = 7