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ryzh [129]
3 years ago
13

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

Mathematics
1 answer:
sertanlavr [38]3 years ago
5 0

Answer:

AC ≈ 11.0 cm

Step-by-step 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 = \sqrt{15}

-------------------------------------------------------

AE² + DE² = DA²

AE² + 7² = 10²

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

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

AE = \sqrt{51}

Then

AC = AE + CE = \sqrt{15} + \sqrt{51} ≈ 11.0 cm ( to the nearest tenth )

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