Question

why triangle formed will given length will be a right angled triangle

Answer 1

Given that the triangle is a right triangle, we only know for sure two things

The length of one sideThat a2+b2=c2a2+b2=c2

Knowing trig functions won’t help too much because you aren’t given an angle (that makes sin hard)

Here’s the proof on why you can’t:

Case 1. You know a (or b)

Given side a, you do not know b or c, solving for a,

a=c2−b2−−−−−−√a=c2−b2

which allows c and b to be many possible things, for example, if a = 3,

3=c2−b2−−−−−−√3=c2−b2

c and b can be 4 and 5 respectively, 10−−√10 and 11 respectively, \sqrt11sqrt11 and 2–√2 respectively, or anything else as long as c2−b2c2−b2 is equal to 9.

Case 2. You know c

c=a2+b2−−−−−−√c=a2+b2

this also allows for a lot of flexibility, for example, is c = 5

a and b can be 3 and 4 respectively, 20−−√20 and 5–√5 respectively, 21−−√21 and 4–√4 respectively, or anything as long as a2+b2a2+b2 is equal to 25.

To those who think that in certain cases you can figure it out by special triangles, that is assuming that all three sides are integers. For example, in a triangle with a hypotenuse of 13, the legs CAN be 5 and 12, but they don’t HAVE to be. They can also be 168−−−√168 and 11, or anything as long as the legs satisfy:

c=a2+b2−−−−−−√c=a2+b2.

Answer 2

✍✍HERE IS YOUR ANSWER...⬇⬇
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$\underline{ANSWER}$ ➡

$<b>The length of sides by 3 cm , 4 cm and 5 cm will formed a right angled triangle. Because the measures of the length of the sides verifies PYTHAGORAS THEOREM.$

$\underline{CHECKING}$ ➡

$<b>Let ,$

$<b>Hypotenues = 5 cm$

$<b>Base = 4 cm$

$<b>Altitude = 3 cm$

$<b>From Pythagorus Theorem ,$

$(Hypotenous) {}^{2} = (Base) {}^{2} + (Altitude) {}^{2} \\ \\ = > (5) {}^{2} = (4) {}^{2} + (3) {}^{2} \\ \\ = > 25 = 16 + 9 \\ \\ = > 25 = 25$

$<b>So , The measures of the length of the sides verifies Pythagorous Theorem.That is why the triangle formed by these lengths of sides is a Right Angled Triangle.$

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