Answered

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Find each unknown side length of the triangle. (Enter your answers in simplified radical form as Xsqrt(Y) .) the traingle hypothenus is 12 and it is a 45,45,90 triangle

Sagot :

MrRoyal

Answer:

[tex]x = 6\sqrt{2}[/tex]

Step-by-step explanation:

Given

[tex]H = 12[/tex] --Hypotenuse

Required

Calculate the unknown side length s

In a 45, 45, 90 triangle, the other side lengths are equal i.e.

Opposite = Adjacent.

Represent these side lengths with x.

Using Pythagoras theorem, we have:

[tex]Adj^2 + Opp^2 = Hyp^2[/tex]

[tex]x^2 + x^2 = 12^2[/tex]

[tex]2x^2 = 144[/tex]

Divide both sides by 2

[tex]x^2 = 72[/tex]

Take square roots of both sides

[tex]x = \sqrt{72[/tex]

Expand

[tex]x = \sqrt{36} * \sqrt{2}[/tex]

[tex]x = 6 * \sqrt{2}[/tex]

[tex]x = 6\sqrt{2}[/tex]

Hence, the other side lengths are: [tex]6\sqrt{2}[/tex]

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