Answer:
(2)
x = 12
y = 4√5
(3)
x = √2
y = √3
z = 2
Explanation:
All of the triangles are right triangles so we can use the pythagorean theorem (a² + b² = c²) to solve for the missing sides.
a = side
b = side
c = hypotenuse (opposite side of right angle)
(2)
First, find x.
x² + 5² = 13²
x² = 144
x = 12
Then use the x value and solve for y.
y² + 8² = 12²
y² = 80
y = √80 or 4√5
(3)
Use the same pythagorean theorem in question 2.
Start with the leftmost triangle and solve for x first.
1² + 1² = x²
x² = 2
x = √2
Now find y
√2² + 1² = y²
y² = 3
y = √3
Lastly, solve for z.
1² + √3² = z²
z² = 4
z = 2