The legs of a right triangle are 6 and 8 cm. Find the hypotenuse and the area of the triangle.

calcific5z
2022-09-12
Answered

The legs of a right triangle are 6 and 8 cm. Find the hypotenuse and the area of the triangle.

You can still ask an expert for help

asked 2022-07-03

How does the Pythagorean theorem describe a circle?

The Pythagorean theorem states, for a right triangle with legs a,b and hypotenuse c,

${a}^{2}+{b}^{2}={c}^{2}$

By replacing c with r, radius this equation becomes the equation of circle at centre (0,0).

How does Pythagoras' equation end up describing the circle?

The Pythagorean theorem states, for a right triangle with legs a,b and hypotenuse c,

${a}^{2}+{b}^{2}={c}^{2}$

By replacing c with r, radius this equation becomes the equation of circle at centre (0,0).

How does Pythagoras' equation end up describing the circle?

asked 2022-07-11

pythagorean theorem extensions

are there for a given integer N solutions to the equations

$\sum _{n=1}^{N}{x}_{i}^{2}={z}^{2}$

for integers ${x}_{i}$ and zan easier equation given an integer number 'a' can be there solutions to the equation

$\sum _{n=1}^{N}{x}_{i}^{2}={a}^{2}$

for N=2 this is pythagorean theorem

are there for a given integer N solutions to the equations

$\sum _{n=1}^{N}{x}_{i}^{2}={z}^{2}$

for integers ${x}_{i}$ and zan easier equation given an integer number 'a' can be there solutions to the equation

$\sum _{n=1}^{N}{x}_{i}^{2}={a}^{2}$

for N=2 this is pythagorean theorem

asked 2022-06-23

Euclidean norm vs pythagorean theorem?

I recently stumbled upon an Euclidian norm. First I thought there are the powers and square root to deal with possible negative values (like in Standard deviation formula) but then I realized, the final number (sum of squares and square root of it) is not same as sum of absolute numbers.

So then I noticed it is more related to Pythagorean theorem (Euclidian distance).

But if looked in google for PT in 3d space i found the formula like

$({a}^{2}+{b}^{2}+{c}^{2}{)}^{\frac{1}{2}}$

But in the Euclidian norm it is

$SQRT({a}^{2}+{b}^{2}+{c}^{2})$

How comes, it is different?

Second question, how comes that the theorem works for any count of dimensions?

I recently stumbled upon an Euclidian norm. First I thought there are the powers and square root to deal with possible negative values (like in Standard deviation formula) but then I realized, the final number (sum of squares and square root of it) is not same as sum of absolute numbers.

So then I noticed it is more related to Pythagorean theorem (Euclidian distance).

But if looked in google for PT in 3d space i found the formula like

$({a}^{2}+{b}^{2}+{c}^{2}{)}^{\frac{1}{2}}$

But in the Euclidian norm it is

$SQRT({a}^{2}+{b}^{2}+{c}^{2})$

How comes, it is different?

Second question, how comes that the theorem works for any count of dimensions?

asked 2022-05-08

Find the length of base of a triangle without using Pythagorean Theorem

I'm curious whether it is possible to find the length of base of the triangle without using Pythagorean Theorem

No Pythagorean Theorem mean:

=> No trigonometric because trigonometric is built on top of Pythagorean Theorem. etc $\mathrm{sin}\theta =\frac{a}{r}$

=> No Integration on line or curve because the integration is built on top of Pythagorean Theorem. etc: $s(x)=\int \sqrt{{f}^{\prime}(x{)}^{2}+1}$

I'm curious whether it is possible to find the length of base of the triangle without using Pythagorean Theorem

No Pythagorean Theorem mean:

=> No trigonometric because trigonometric is built on top of Pythagorean Theorem. etc $\mathrm{sin}\theta =\frac{a}{r}$

=> No Integration on line or curve because the integration is built on top of Pythagorean Theorem. etc: $s(x)=\int \sqrt{{f}^{\prime}(x{)}^{2}+1}$

asked 2022-05-07

which axiom(s) are behind the Pythagorean Theorem

There are many elementary proofs for the Pythagorean Theorem, but no matter they use areas, similarities, even algebraic proofs, it is not straightforward to tell why it is true tracing back to the (Euclidean geometry) axioms. Are all these proofs equivalent? Do they all track back to the same axioms?

There are many elementary proofs for the Pythagorean Theorem, but no matter they use areas, similarities, even algebraic proofs, it is not straightforward to tell why it is true tracing back to the (Euclidean geometry) axioms. Are all these proofs equivalent? Do they all track back to the same axioms?

asked 2022-06-23

Why is the Pythagorean Theorem not the Pythagorean Law?

Why do we call the Pythagorean Theorem a theorem, not a law?

As far as I know, we call a theorem a theorem because though it's reliable in every observable case, its truthfulness cannot be proven for every case. However I've looked and it seems as though we (as the human race) have very extensive proofs of the Pythagorean Theorem, considering every case. Why is it that it hasn't made the transition from theorem to law? Is my terminology confused? Is it not as proven as I think it is? Is there some other condition for being a law that I don't know about?

Why do we call the Pythagorean Theorem a theorem, not a law?

As far as I know, we call a theorem a theorem because though it's reliable in every observable case, its truthfulness cannot be proven for every case. However I've looked and it seems as though we (as the human race) have very extensive proofs of the Pythagorean Theorem, considering every case. Why is it that it hasn't made the transition from theorem to law? Is my terminology confused? Is it not as proven as I think it is? Is there some other condition for being a law that I don't know about?

asked 2022-07-05

Algebra Logical Pythagorean theorem help

A wire is attached to the top of a pole. The pole is 2 feet shorter than the wire, and the distance from the wire on the ground to the bottom of the pole is 9 feet less than the length of the wire. Find the length of the wire and the height of the pole.

Hint: Use the pythagorean theorem then set up a quadratic equation equal to zero and solve. I got c=17 and c=5 but I don't know what the length of the wire is or the height of the pole.

A wire is attached to the top of a pole. The pole is 2 feet shorter than the wire, and the distance from the wire on the ground to the bottom of the pole is 9 feet less than the length of the wire. Find the length of the wire and the height of the pole.

Hint: Use the pythagorean theorem then set up a quadratic equation equal to zero and solve. I got c=17 and c=5 but I don't know what the length of the wire is or the height of the pole.