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DiKsa [7]
3 years ago
9

Please assist me with this problem​

Mathematics
2 answers:
timurjin [86]3 years ago
7 0

Answer:

y = sqrt(5)

x = sqrt(10)

Step-by-step explanation:

y = sqrt(5)

Opposite angles are equal

x is the hypotenuse

x² = 5 + 5

x² = 10

x = sqrt(10)

Verizon [17]3 years ago
3 0
<h3>Answers:</h3><h3>x = sqrt(10)</h3><h3>y = sqrt(5)</h3>

============================================

Explanation:

Naturally I start with x as that letter precedes y in the alphabet; however, it's easier to start with y because it is a leg of this triangle. We will then use the value of y to find x later.

For any 45-45-90 triangle, the two legs are the same length. So that's why we're able to quickly see that y = sqrt(5)

To get the hypotenuse, we multiply the leg length by sqrt(2). This trick only works for 45-45-90 triangles.

hypotenuse = leg*sqrt(2)

x = sqrt(5)*sqrt(2)

x = sqrt(5*2)

x = sqrt(10)

The rule I used is sqrt(a)*sqrt(b) = sqrt(a*b)

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

An alternate path is to use the pythagorean theorem to find x

a^2+b^2 = c^2

(sqrt(5))^2 + (sqrt(5))^2 = x^2

5 + 5 = x^2

10 = x^2

x^2 = 10

x = sqrt(10)

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\displaystyle \large{ {y}^{2}  = x} \\  \displaystyle \large{ y =  \pm  \sqrt{x} }

Looks like we can use any x-values right? Nope.

The value of x only applies to any positive real numbers for one reason.

As we know, any numbers time itself will result in positive. No matter the negative or positive.

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\displaystyle \large{  {a}^{2}  = a \times a =  |b| }

Where b is the result from a×a. Let's see an example.

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\displaystyle \large{  {2}^{2}  = 2 \times 2 = 4} \\  \displaystyle \large{  {( - 2)}^{2}  = ( - 2) \times ( - 2) =  | - 4|  = 4}

So basically, their counterpart or opposite still gives same value.

Then you may have a question, where does √-1 come from?

It comes from this equation:

\displaystyle \large{   {y}^{2}  =  - 1}

When we solve the quadratic equation in this like form, we square both sides to get rid of the square.

\displaystyle \large{   \sqrt{ {y}^{2} } =   \sqrt{ - 1}  }

Then where does plus-minus come from? It comes from one of Absolute Value propety.

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Then we have the square root of -1 in negative and positive. But something is not right.

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It is one of the solution from the equation y^2 = 1.

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So what is the different? The different between two numbers is that √-1 does not exist in a real number system since any squared numbers only result in positive while -√1 is one of the solution from y^2 = 1 and exists in a real number system.

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