Question

Calculate the length of AC, to the nearest tenth of a centimeter.

Answer 1

AC ≈ 11.0 cm

Explanation:

Using Pythagoras' identity in Δ CDE and Δ ADE

CE² + DE² = DC²

CE² + 7² = 8²

CE² + 49 = 64 ( subtract 49 from both sides )

CE² = 15 ( take the square root of both sides )

CE =
`√(15)`

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AE² + DE² = DA²

AE² + 7² = 10²

AE² + 49 = 100 ( subtract 49 from both sides )

AE² = 51 ( take the square root of both sides )

AE =
`√(51)`

Then

AC = AE + CE =
`√(15)` +
`√(51)` ≈ 11.0 cm ( to the nearest tenth )