Answer:
x = 26.5
y = 12.0
z = 13.4
Step-by-step explanation:
✔️To find x, apply the leg rule, which is:
Hypotenuse/leg = leg/part
Hypotenuse = 30
Leg = x
Part = 30 - 6 = 24
Plug in the values into the equation
30/x = x/24
Cross multiply
x² = 30*24
x² = 720
x = √720
x = 26.5 (nearest tenth)
✔️Apply the triangle altitude theorem to find y:
Based on the theorem, h = √(ab)
Where,
a = 6
b = 30 - 6 = 24
h = y
Plug in the values
y = √(6*24)
y = √144
y = 12
✔️Apply the leg rule, Hypotenuse/leg = leg/part to find z:
Hypotenuse = 30
Leg = z
Part = 6
Plug in the values into the equation
30/z = z/6
Cross multiply
z² = 30*6
z² = 180
z = √180
z = 13.4 (nearest tenth)
