Question

The length of the hypotenuse of a 45°-45°-90° triangle is 8 units. Find the exact value of the length of the leg.

Answer 1

Use the Pythagorean theorem to write an equation. Then solve it for a.

Answer 2

8^2 - a^2 = a^2

Answer 3

add a^2 to both sides, and it becomes 8^2 = a^4

Answer 4

\[a = \frac{1}{\sqrt2} \times 8 =\frac{1}{\sqrt2} \times 4 \times 2\]
\[=\frac{1}{\sqrt2} \times 4 \times \sqrt 2 \times \sqrt 2 = 4 \sqrt2 units\]

Answer 5

Thanks!

Answer 6

\(a^2 + a^2 = 8^2\)

\(2a^2 = 64\)

\(a^2 = 32\)

\(a = \sqrt{32} \)

\(a = \sqrt{16 \cdot 2} \)

\(a = \sqrt{16} \cdot \sqrt{2} \)

\(a = 4\sqrt{2} \)

Answer: the leg is \(4\sqrt{2}\) units long.

Answer 7

Thanks!

Answer 8

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