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

Question

mathstudent55 · Answer

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

8^2 - a^2 = a^2

deadshot · Answer

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

anonymous · Answer

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

deadshot · Answer

Thanks!

mathstudent55 · Answer

$a^2 + a^2 = 8^2$

$2a^2 = 64$

$a^2 = 32$

$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.

deadshot · Answer

Thanks!

mathstudent55 · Answer

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