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3 years ago

Which group of three squares will form a right triangle when joined at their vertices?

Mathematics

1 answer:

Ilia_Sergeevich [38]3 years ago

8 0

Answer:

Option ?) 17 cm, 15 cm, 8 cm

The assignment should have four options to choose from, but there is only a picture of two.

Step-by-step explanation:

None of the squares shown form a right triangle. To determine if sides form a right triangle, you use this formula:

a²+b²=c²

We are given two options in the picture.

Option A) 18, 10, and 8.

Option B) 12, 9, and 6.

So, now we need to apply the formula:

Option A)

║8² + 10² = 18²

↓

║64 + 100 = 324

↓

║FALSE

Option B)

║6² + 9² = 12²

↓

║36 + 81 = 144

↓

║FALSE

Both of these options are false. But, I decided to look up this assignment to check my answer. It turns out, there are 4 options, and you only had a picture of two. So, what's the answer?

There is an answer choice that shows 3 squares with the lengths of 17 cm, 15 cm, and 8 cm. This is the correct answer.

For proof, let's apply the formula:

Option ?)

║8² + 15² = 17²

↓

║64 + 225 = 289

↓

║TRUE

[Since the option isn't shown, I'll put a '?' so there is no confusion]

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\\\\\\
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\\\\\\
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-------------------------------\\\\
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$\bf 8sin^4(x)-6sin^2(x)+1=0\implies 8[~[sin(x)]^2~]^2-6[sin(x)]^2+1=0
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~~~~~~~~~~~~\textit{quadratic formula}
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& 8 sin^4& -6 sin^2(x)& +1\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array} 
\qquad \qquad 
sin(x)= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}
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\begin{cases}
\frac{1}{2}\\\\
\frac{1}{4}
\end{cases}$

$\bf \measuredangle x=
\begin{cases}
sin^{-1}\left( \frac{1}{2} \right)
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\begin{cases}
\frac{\pi }{6}~,~\frac{5\pi }{6}\\
----------\\
\approx~0.252680~radians\\
\qquad or\\
\approx~14.47751~de grees\\
----------\\
\pi -0.252680\\
\approx 2.88891~radians\\
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