The calculated values of x and y are x = 8√5 and y = 8√15
How to determine the values of x and y
From the question, we have the following parameters that can be used in our computation:
The right triangle
Given that the triangle to the left is a 45-45-90 triangle
Then
Leg = Hypotenuse/√2
Substitute the known values into the equation
Leg = 16√10/√2
Evaluate
Leg = 16√5
The values of x and y are then calculated using the following sine ratio
sin(30) = x/Leg
cos(30) = y/Leg
So, we have
x = Leg * sin(30)
y = Leg * cos(30)
Substitute the known values into the equation
x = 16√5 * sin(30)
y = 16√5 * cos(30)
Evaluate
x = 8√5
y = 8√15
Hence, the values of x and y are x = 8√5 and y = 8√15