Answer:
The value of x = 0.5, y = 0.8 and z = 0.9
Step-by-step explanation:
From the given figure. Let's form the equations
50z + 13 + 45x + [tex]\frac{19}{2}[/tex] = 90°
45x + 50z + 13 + 9.5 = 90
45x + 50z + 22.5 = 90
45x + 50z = 90 - 22.5
45x + 50z = 67.5 --------------------------(1)
[tex]\frac{225y}{2} = 90[/tex]° Because it is a right angle.
225y = 180
y = [tex]\frac{180}{225}[/tex]
y = 0.8 --------------------(2)
44x + 125y + 80z -14 = 180° because they are supplementary angles add upto 180 degrees.
44x + 125y + 80z = 180 + 14
44x +125y + 80z = 194 ------------(3)
Now plug in y = 0.8 in the above equation (3), we get
44x + 125 times 0.8 + 80z = 194
44x + 100 + 80z = 194
44x + 80z = 194 - 100
44x + 80z = 94 ---------------------(4)
Now let's solve the equation (1) and (4) using elimination method.
x = 0.5
Now plug in x = 0.5 in the equation (4) and find the value of z
44(0.5) + 80z = 94
22 + 80z = 94
80z = 94 - 22
80z = 72
z = [tex]\frac{72}{80}[/tex]
z = 0.9
Therefore, the value of x = 0.5, y = 0.8 and z = 0.9
