Triangle Definition and 1000 Threads

Hello everyone, I am trying to solve exercise 7.21 in the "Hobson, Efstathiou, Lasenby, General Relativity. An introduction for physicists." What is asked is to show that the parallel transportation of a vector, along a closed triangle on a 2-sphere, results in an vector orthogonal to the...

I think we can say that a straight line is a triangle in which sum of two side equals third side in which two angle equals 0° and the middle angle equals 180°, but can we say that a striaght line is a triangle with two angle equals 90°, I am saying this because my sister is not beliving that...

Can you suggest a book that discusses properties of triangles and circles? (Like properties and theorems on circumcircle, excircle, nine point circle, etc). Most of the geometry books are either to basic or too advanced. I have read a book on complex numbers by Liang Shin Hahn. But the...

Homework Statement kettletown is 27km from teatown and 32km from coffee town. The angle from kettletown to coffee town to teatown is 29o. Determine the two possible distances between teatown and coffee town. Homework EquationsThe Attempt at a Solution The only problem I'm having is trying to...

Given: A right triangle and all the sides of the triangle are whole numbers. Does this imply that all the sides of the triangle can only be found by using the Pythagorean triple formula? Another words, is it possible that a right triangle can exist with whole number sides that escape the...

Let $\alpha,\,\beta$ and $\gamma$ be the interior angles of an acute triangle. Prove that if $\alpha \lt \beta \lt \gamma$, then $\sin 2\alpha \gt \sin 2\beta \gt \sin 2\gamma$.

Homework Statement Evaluate ∫∫D sin(x) / x dA, where A is the triangle with vertices (0, 0),(0, 1),(1, 1). Homework EquationsThe Attempt at a Solution I've set up the integral, with x≤y≤x^2, 0≤x≤1 for the upper and lower bands of each integral. dxdy I'm not sure how to go about it though. I...

Homework Statement A dielectric equilateral triangle of dielectric constant 30 is inserted into uniform horizontal electric field of 100,000 N/C. What is the potential difference between two points 3 cm apart on one of the sides? Homework Equations ΔV =∫E⋅dl E' =E/κ The Attempt at a...

In a triangle $ABC$ with side lengths $a,\,b$ and $c$, it's given that $17a^2+b^2+9c^2=2ab+24ac$. Evaluate $\cos \angle B$.

Hi PF! A friend asked me to look at a problem, said it was on his mind. Rather than restate it here (since a picture helps) please check out the attachment. I drew a picture in tikZ and gave my attempt at a solution, but something in my gut feels the answer is infinite. I'd love to talk with...

Homework Statement Magnetic Field B is going into the plane. Bar is moving to the right with velocity v. Neglect resistance of the conducting bar and all contacts. a.) Determine the induced emf in the circuit. b.) To maintain the uniform motion of the conductive bar, there must be an external...

$\triangle ABC,\angle B=30^o , \,\,and \,\, \overline{BC}^2 - \overline{AB}^2=\overline{AB}\times \overline{AC}\\ find \,\, \angle C=?$

Homework Statement Three equal charges with charge q and mass m are placed into an equilateral triangle of side length L. Find the speed of each when they are infinitely far from one another. Homework Equations -ΔU =ΔK (since the electric force is conservative), U= 1/4πε Σq1q2 /r The...

Homework Statement two particles with charges 4e and -4e are fixed at the vertices of an equilateral triangle with sides of length a. If k=1/4 pi Ԑ what quantity of work is required to move a particle with a charge q from the other vertex to the center of the line joining the fixed charges...

Homework Statement Given points of a triangle: A(4,1,-2),B(2,0,0),C(-2,3,-5). Line p contains point B, is orthogonal to \overline{AC}, and is coplanar with ABC. Intersection of p and \overline{AC} is the point B_1. Find vector \overrightarrow{B_1B}. Homework Equations -Vector projection - Dot...

Given an Isosceles triangle with the area of 100 with internal angles of $$40^o, 70^o,70^o$$ $A=\frac{1}{2}bh$ so $100=\frac{1}{2}\left(z\sin\left({70^O}\right)\right)\left(2z\cos\left({70^o}\right)\right)$ $z$ is length of one the equal sides At least started here

Let $a\,b$ and $c$ be the sides of a triangle. Prove that \frac{a}{b+c-a}+\frac{b}{a+c-b}+\frac{c}{a+b-c}\ge 3.

I believe I could work this problem fine had the instructor not placed statements #3,4, and 6, as well as the reasons # 5 and 7. I can't seem to understand where he's using the transitive property in #5. If these steps weren't here I would assume, I'm only using substitution to prove that "RS"...

Homework Statement Air (assumed incompressible) flows across the rotor shown in the figure such that the magnitude of the absolute velocity increases from 15 m/s to 25 m/s. Measurements indicate that the absolute velocity at the inlet is in the direction shown. Determine the direction of the...

What would the angular velocity for a phasor be for a triangle wave? I think it would vary sinusoidally but I can't find an expression

Hello everyone. I'm learning Trigonometry right now with myself and at current about how to find the trigonometric ratio of the angle (90° + θ) in terms of θ. I'm quite confused in the Figure. How sin(90° + θ) become equal to sin (90° - θ) of triangle P'OM'. I know that triangle P'OM' and POM...

Prove that there exists a triangle which can be cut into 205 congruent triangles.

Homework Statement In triabgle ABC, AB = 2x cm, AC = x cm, BC = 21 cm and angle BAC = 120 degrees. Calculate the value of x? Homework Equations I used the cosine rule here The Attempt at a Solution As we have 2 sides and an angle I used the cosine rule - Am I correct? (2) means squared b(2)...

Homework Statement At the vertices of a triangle there are + 5C, -7C, -3C of charge respectively. What is the electric intensity and direction at its orthocentre? Homework Equations Each side of the triangle is 1 mm in length. The Attempt at a Solution [/B] I failed to find the distance of...

Write the following formulas: a) The minimum perimeter of any triangle (abc) only known heights corresponding to the sides a and b. b) The maximum height and minimum corresponding to the side b of any triangle (abc) only known the value of its perimeter and height corresponding to the side a.

Write the following formulas: a) The minimum perimeter of any triangle (abc) only known heights corresponding to the sides a and b. b) The maximum height and minimum corresponding to the side b of any triangle (abc) only known the value of its perimeter and height corresponding to the side a.

Calculate the area of a triangle knowing its 3 heights ha = 3 m hb = 4 m hc = 5 m NOTE = You can use the online triangle calculator TrianCal to see and draw the results. NOTE = Do not use the values ??of responses. A) 10.03 m2 B) 10.04 m2 C) 10.05 m2 D) Imposible

Calculate the area of a triangle knowing its perimeter and 2 heights perimeter = 30 m ha = 8 m hb = 9 mNOTE = You can use the online triangle calculator TrianCal to see and draw the results. NOTE = Do not use the values ??of responses. A) 41.29 m2 B) 42.93 m2 or 36.28 m2 C) 42.95 m2 or 36.29...

That value has to have one side of a triangle to be isosceles knowing its perimeter and area. Area = 40 m2 Perimeter = 30m NOTE = You can use the online triangle calculator TrianCal to see and draw the results. NOTE = Do not use the values ??of responses. A) 13.33 m B) 19.18 m or 4.54 m C)...

Calculate the sides of a triangle knowing its area, perimeter and angle A. Area = 30 m2 Perimeter = 30m Angle A = 30º NOTE = You can use the online triangle calculator TrianCal to see and draw the results. NOTE = Do not use the values ??of responses. A) 6.09, 9.36 and 14.55 B) 7.40, 8.63 and...

Homework Statement The triangle formed by the tangents to the parabola y2=4ax, at the ends of the latus rectum and the double ordinate through it's focus is: 1) equilateral 2) acute angles isosceles 3)right angled isosceles 4) dependent on value of a Homework Equations...

Homework Statement http://i.stack.imgur.com/KzCIl.png From the given picture the known quantities are: ##r = 7*3^{1/2} ## ##BC = 13 ## angle opposite to AC is ##120 ## degrees Homework Equations 3. The Attempt at a Solution [/B] I figured i could use a sine rule to get the side ##AC ##...

Homework Statement Given the isosceles triangle whose sides are : c=10 b=13 find the are of a square drawn inside the triangle whose upper edges touch the b sides of the triangle. Homework Equations 3. The Attempt at a Solution [/B] I named the side of the square a. First i made two equations...

Not sure how to solve considering nothing is given as perpendicular or bisected. Is anyone aware on how to solve this problem? ~S.R.K.

Homework Statement The tangent line of a curve y=e^(-x) intercepts the axises at points A and B. What is the maximum area of a triangle AOB considering O as the origin. Homework Equations Ar= xy/2 The Attempt at a Solution Derivative of this function is y'=-e^(-x) I took the formula of the...

Homework Statement Prove that if a right triangle has all sides rational and primitives (co-primes), then one of the smaller side must be even number. Homework Equations For a right triangle (a,b,c) with c is the hypotenuse. $$a^2+b^2=c^2$$ The Attempt at a Solution In order to create a...

Folks, I am puzzled how one obtains equation 3.2.31 based on the schematic as attached! Can you help? Is there an online source I can refer to to learn how to obtain angles and magnitudes of complex schematics? Thanks

Hi, Can somebody please point me into a direction how to solve the attached trig problem? First step, where can I find such values for sin (alpha)?Thanks.

Homework Statement Suppose the isosceles prism of the figure(http://imgur.com/EQiQSoO) has apex angle φ = 53.4° and index of refraction n = 1.41. (a) What is the smallest angle of incidence θ for which a ray can enter the left face of the prism and exit the right face? (b) What angle of...

I'm not really sure if this is true, which is why I want your opinion. I have been trying to prove it, but it will help me a lot if someone can confirm this. Let ## v_{1}, v_{2} ... v_{n} ## be vectors in a complex inner product space ##V##. Suppose that ## | v_{1} + v_{2} +...+ v_{n}| =...

Find the lengths of the sides of a triangle with 14, 22 and 28 as the lengths of its altitude.

I found this question in my study guide triangle ABC is similar to triangle DEF. Triangle ABC has sides 4,6,8. Wich could be the corresponding sides of a triangle DEF? Indicate all that apply A) 1, 1.5, 2 B)1.5, 2.25, 3 C)6, 9, 12 D) 8, 12, 16 E)10, 15, 20 What I did was add the...

Hi, I'm trying to solve this exercize : I/3 charges Q, positives, are at the corner of an equilateral triangle of centre O, in (x,O,y) . We want to compute the electric field created by the 3 charges on the axis z, passing by O and perpendicular at (x,O,y), thus computing the electric field...

In the triangle a point I is a centre of inscribed circle. A line AI meets a segment BC in a point D. A bisector of AD meets lines BI and CI respectively in a points P and Q. Prove that heights of triangle PQD meet in the point I. I've tried to show that sides of triangle PQD are parallel to...

Let ${y}_{n}$ be a arbitrary sequence in X metric space and ${y}_{m+1}$ convergent to ${x}^{*}$ in X...İn this case by using triangle inequality can we say that ${y}_{n}\to {x}^{*}$

Homework Statement a thin uniform wire is bent to form two equal sides AB and AC of triangle ABC , where AB=AC=5cm . the third side BC , of length 6cm is made from uniform wire of twice the density of the first . the distance of centre of mass from A is ? Homework Equations x centre of mass...

For the triangle shown in the below image, ##\sin 60° = \frac{opposite}{hypotenuse} = \frac{y}{r}## ##\sin 30° = \frac{opposite}{hypotenuse} = \frac{x}{r}## The questions are: 1. What is the opposite and hypotenuse of sin 90°? 2. I am guessing that the opposite and hypotenuse of sin 90 is r...

Hello, Suppose that I have two triangles ##\bigtriangleup ABC## and ##\bigtriangleup XYZ## that are known to be congruent by the side-side-side axiom, from which it follows that the parts are also congruent, such as the angles. My question is, how do I determine which of the three angles of...

Homework Statement What is the area of a triangle on Earth that goes from the North Pole down to the equator, through the prime meridian, across the equator to 30 degrees east longitude, then back up to the equator? The radius of the Earth is about 6378 km. Homework Equations alpha + beta +...

In the triangle ABC the point D lies on the side BC and point E on the side AB. BD = AC, AD = AE and AB ^ 2 = AC * BC. Show that \angle BAD = \angle CEA