Question

Pls help me I keeping getting it wrong

Answer 1

z =
`√(60)` ≈ 7.7 cm

Explanation:

We can solve for the length of side z using the Pythagorean Theorem:

→ a² + b² = c²

where a and b are the lengths of the right triangle's legs (its shorter sides), and c is the length of the hypotenuse (its longest side).

We are given the following values in the diagram:

• a = 2 cm
• c = 8 cm

Using these values, we can solve for the length of the side labeled z, which is equivalent to b in the formula for the Pythagorean Theorem:

a² + b² = c²

↓ plugging in the given values

2² + z² = 8²

↓ rewriting the exponents

(2 × 2) + z² = (8 × 8)

↓ executing the multiplication

4 + z² = 64

↓ subtracting 4 from both sides

z² = 60

↓ taking the square root of both sides

z =
`\bold{√(60)}` cm

↓ evaluating using a calculator (and rounding to 1 decimal place)

z ≈ 7.7 cm