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Olin [163]
1 year ago
11

Course 3 chapter 5 triangles and the pythagorean theorem

SAT
1 answer:
Galina-37 [17]1 year ago
5 0

The pythagorean theorem is used to calculate the lengths of a right triangle

The hypotenuse of the triangle is 6.5 cm

<h3>How to determine the hypotenuse of the triangle?</h3>

From the complete question, we have the following side lengths

  • Opposite = 5.7 cm
  • Adjacent = 3.2 cm

The hypotenuse of the triangle is then calculated as:

Hypotenuse^2 = Opposite^2 + Adjacent^2

This gives

Hypotenuse^2 = 3.2^2 + 5.7^2

Evaluate the sum

Hypotenuse^2 = 42.73

Take the square root of both sides

Hypotenuse = 6.5

Hence, the hypotenuse of the triangle is 6.5 cm

Read more about hypotenuse at:

brainly.com/question/654982

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Answer:

In the form of a+\sqrt{b},

  • a = 3
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Explanation:

The equation can be rewritten as:

x^{2} -6x-4=0

Find the solutions using the quadratic formula:

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x=\frac{-b+-\sqrt{b^{2}-4ac} }{2a} \\\\=\frac{-(-6)+-\sqrt{(-6)^{2} -4(1)(-4)} }{2(1)} \\\\=\frac{6+-\sqrt{36+16} }{2} \\\\=\frac{6+-\sqrt{52} }{2} \\\\=\frac{2(3)+-2\sqrt{13} }{2} \\\\=\left \{ {{x_{1}=3+\sqrt{13} } \atop {x_{2}=3-\sqrt{13} }} \right.

Find the solution that's positive:

\left \{ {{x_{1} = 3+\sqrt{13} = 6.605551275... } \atop {x_{2} = 3-\sqrt{13} = -0.605551275... }} \right

Therefore, the solution would be 3+\sqrt{13}.

In the form of a+\sqrt{b},

  • a = 3
  • b = 13
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