Recent questions in Pythagorean Theorem

High school geometryAnswered question

Hayley Steele 2023-02-26

Two congruent circles with centres at (2,3) and (5,6), which intersect at right angles, have radius equal to?

High school geometryAnswered question

Theresa Daugherty 2022-12-16

State whether the given statement is true or false: 9, 40, 41 is a Pythagorean triplet. True or false

High school geometryAnswered question

nefg4m 2022-12-16

5, 12, 13 is a Pythagorean triplet. True or false

High school geometryAnswered question

hEorpaigh3tR 2022-12-02

Based on Pythagorean identities, which equation is true?

A. ${\mathrm{sin}}^{2}\theta -1={\mathrm{cos}}^{2}\theta $

B. ${\mathrm{sec}}^{2}\theta -{\mathrm{tan}}^{2}\theta =-1$

C. -${\mathrm{cos}}^{2}\theta -1={\mathrm{sin}}^{2}\theta $

D. ${\mathrm{cot}}^{2}\theta -{\mathrm{csc}}^{2}\theta =-1$

A. ${\mathrm{sin}}^{2}\theta -1={\mathrm{cos}}^{2}\theta $

B. ${\mathrm{sec}}^{2}\theta -{\mathrm{tan}}^{2}\theta =-1$

C. -${\mathrm{cos}}^{2}\theta -1={\mathrm{sin}}^{2}\theta $

D. ${\mathrm{cot}}^{2}\theta -{\mathrm{csc}}^{2}\theta =-1$

High school geometryAnswered question

Scarlet Marshall 2022-12-02

The end rollers of bar AB(1.5R) are constrained to the slot. If roller A has a downward velocity of 1.2 m/s and this speed is constant over a small motion interval, determine the tangential acceleration of roller B as it passes the topmost position. The value of R is 0.5 m.

High school geometryAnswered question

umthumaL3e 2022-11-26

The area of the obtuse angle triangle shown below is:

A17.5 sq. units

B 25 sq. units

C 14 sq. units

D 15 sq. units

A17.5 sq. units

B 25 sq. units

C 14 sq. units

D 15 sq. units

High school geometryAnswered question

autreimL8 2022-11-25

Replacing x with $\frac{1}{2}$ in $2{x}^{2}$ will give you an answer of 1.

High school geometryAnswered question

Neil Sharp 2022-11-24

Why does the Pythagorean theorem only work for right triangles?

High school geometryAnswered question

BertonCO5 2022-11-24

7, 24, 25 is a Pythagorean triplet.

A.True

B.False

A.True

B.False

High school geometryAnswered question

Widersinnby7 2022-11-02

A bicycle wheel with a 5 inch ray rotates ${60}^{\circ}$. What distance has the bicycle traveled?

High school geometryAnswered question

calcific5z 2022-09-12

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

High school geometryAnswered question

Karli Kidd 2022-09-02

Solve for X.

Anlge A=8x+5

Angle B=4${x}^{2}$-10

Angle C=${x}^{2}$+2x+10

I know that they equal 180 degrees. However I am drawinga blank on the factoring part of it

Anlge A=8x+5

Angle B=4${x}^{2}$-10

Angle C=${x}^{2}$+2x+10

I know that they equal 180 degrees. However I am drawinga blank on the factoring part of it

High school geometryAnswered question

obojeneqk 2022-09-01

For each of the following, can the measures represent sides ofa right triangle? Explain your answers.a. 3 m, 4 m, 5 mb. $\sqrt{2cm},\sqrt{3cm},\sqrt{5cm}$

High school geometryAnswered question

on2t1inf8b 2022-07-27

A 10-m ladder is leaning against a building. The bottom of theladder is 5-m from the building. How high is the top of theladder?

High school geometryAnswered question

Ryan Robertson 2022-07-11

Pythagorean theorem and its cause

I'm in high school, and one of my problems with geometry is the Pythagorean theorem. I'm very curious, and everything I learn, I ask "but why?". I've reached a point where I understand what the Pythagorean theorem is, and I understand the equation, but I can't understand why it is that way. Like many things in math, I came to the conclusion that it is that way because it is; math is the laws of the universe, and it may reach a point where the "why" answers itself. So what I want to know is, is there an explication to why the addition of the squared lengths of the smaller sides is equal to the squared hypotenuse, or is it just a characteristic of the right triangle itself? And is math the answer to itself?

Thank you.

I'm in high school, and one of my problems with geometry is the Pythagorean theorem. I'm very curious, and everything I learn, I ask "but why?". I've reached a point where I understand what the Pythagorean theorem is, and I understand the equation, but I can't understand why it is that way. Like many things in math, I came to the conclusion that it is that way because it is; math is the laws of the universe, and it may reach a point where the "why" answers itself. So what I want to know is, is there an explication to why the addition of the squared lengths of the smaller sides is equal to the squared hypotenuse, or is it just a characteristic of the right triangle itself? And is math the answer to itself?

Thank you.

High school geometryAnswered question

kramberol 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

High school geometryAnswered question

sweetymoeyz 2022-07-07

"Pythagorean theorem" for projection onto convex set

I'm going through the book on online convex optimization by Hazan, and in the first chapter I saw this assertion (which Hazan calls the "pythagorean theorem"):

Let $K\subset {\mathbb{R}}^{d}$ be a convex set, $y\in {\mathbb{R}}^{d}$, and $x={\mathrm{\Pi}}_{K}(y)$. Then for any $z\in K$ we have:

$\Vert y-z\Vert \ge \Vert x-z\Vert .$

It is presented without proof - what is a proof for this? Also, how does it relate to the pythagorean theorem?

I'm going through the book on online convex optimization by Hazan, and in the first chapter I saw this assertion (which Hazan calls the "pythagorean theorem"):

Let $K\subset {\mathbb{R}}^{d}$ be a convex set, $y\in {\mathbb{R}}^{d}$, and $x={\mathrm{\Pi}}_{K}(y)$. Then for any $z\in K$ we have:

$\Vert y-z\Vert \ge \Vert x-z\Vert .$

It is presented without proof - what is a proof for this? Also, how does it relate to the pythagorean theorem?

High school geometryAnswered question

Janessa Olson 2022-07-07

Non-geometric Proof of Pythagorean Theorem

Is there a purely algebraic proof for the Pythagorean theorem that doesn't rely on a geometric representation? Just algebra/calculus. I want to TRULY understand the WHY of how it is true. I know it works and I know the geometric proofs.

Is there a purely algebraic proof for the Pythagorean theorem that doesn't rely on a geometric representation? Just algebra/calculus. I want to TRULY understand the WHY of how it is true. I know it works and I know the geometric proofs.

High school geometryAnswered question

2d3vljtq 2022-07-06

The Pythagorean theorem and Hilbert axioms

Can one state and prove the Pythagorean theorem using Hilbert's axioms of geometry, without any reference to arithmetic?

Edit: Here is a possible motivation for this question (and in particular for the "state" part of this question). It is known that the theory of Euclidean geometry is complete. Every true statement in this theory is provable.

On the other hand, it is known that the axioms of (Peano) arithmetic cannot be proven to be consistent. So, basically, I ask if there is a reasonable theory which is known to be consistent and complete, and in which the Pythagorean theorem can be stated and proved.

In summary, I guess I am asking - can we be sure that the Pythagorean theorem is true? :)

Can one state and prove the Pythagorean theorem using Hilbert's axioms of geometry, without any reference to arithmetic?

Edit: Here is a possible motivation for this question (and in particular for the "state" part of this question). It is known that the theory of Euclidean geometry is complete. Every true statement in this theory is provable.

On the other hand, it is known that the axioms of (Peano) arithmetic cannot be proven to be consistent. So, basically, I ask if there is a reasonable theory which is known to be consistent and complete, and in which the Pythagorean theorem can be stated and proved.

In summary, I guess I am asking - can we be sure that the Pythagorean theorem is true? :)

Contrary to the popular belief, the majority of Pythagorean theorem problems are also encountered by the engineers and designers who are majoring in all the possible subjects. While there are questions that you have to master as a high school student, it's often necessary to come back to the basics and take a closer look at the answers that are provided. Likewise, when you know the theorem well and understand how it works, you can become a Pythagorean theorem solver based on these questions alone. Take your time to explore the provided examples and see how exactly these are formed.