Triangle Definition and 1000 Threads

On the internet there is only information on how to get rid of the trianglethat indicates an error in the formula in the cell. But in my workplace I need to upload data to a program and sometimes a successful upload requires that the data in my excel cells be marked by this error-triangle...

Triangle inscribed on circle proof...I am missing something :( Homework Statement I have provided a link to the problem below http://imageshack.us/a/img854/4143/photo1lsd.jpg I need to prove AE is an altitude on this proof Homework Equations all radii are congruent, cpctc, ASA...

Homework Statement a) Find the speed of the boat with respect to the Earth. (km/h) b) Find the speed of the boat with respect to the river if the boat's heading in the water is 60° south east (km/h) Homework Equations v(x) = v cos(θ) v(y) = v sin(θ) v = √(vx^2+vy^2) but can't use it in...

Homework Statement Let a, b and c be the lengths of the sides of a triangle. Suppose that ab + bc + ca = 1. Show that (a+1)(b+1)(c+1) < 4. Homework Equations N/A (Olympiad problem) The Attempt at a Solution I've made a few inroads at this problem, but whether or not they're going...

Homework Statement Prove llxl-lyll≤lx-yl (The triangle inequality: la+bl≤lal+lbl) The Attempt at a Solution For the first part, I assumed lxl≥lyl: lxl=l(x-y)+yl Then, by Triangle Inequality l(x+y)+yl≤l(x-y)l+lyl So, lxl≤l(x-y)l+lyl Subtract lyl from both sides to...

Homework Statement I am trying to find the following (marked in red) angle, I know that the radii to the points of contact make an angle θ with the horizontal. Homework Equations all angles of a triangle add up to 180 degrees. isosceles triangle, has two equivalent sides The...

If you have a Right Triangle and you have one angle, alpha. How do you find the other angle, beta?

Could anyone tell me how they found the area of the triangle? When I try to use 0.5*b*h I get 10.64483443, not 10.5

We got given the formula for finding the centroid of a triangle which was to (\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}) but we the teacher said he didn't have time to show the proof, however I'm still curious. Could anyone possible hint on how I could go about to prove this? My...

Homework Statement Consider a tiling of the unit sphere in ##\mathbb R^3## by equilateral triangles so that the triangles meet full edge to full edge (and vertex to vertex). Suppose n such triangles meet an one vertex. Show that the only possibilities for n are ## n=3 ##, ##n = 4##, or...

Homework Statement Find the geometric image of the complex number z, if z, z^2, z^3 are the vertices of a right triangle. Homework Equations The Attempt at a Solution I tried expanding z^2, z^3, and than using both the pythagoras theorem, and vectors (in separate attempts), but...

Hi, can you please give me some hints to show that \frac{|a-b|}{1+|a|+|b|} \leq \frac{|a-c|}{1+|a|+|c|}+\frac{|c-b|}{1+|c|+|b|}, \forall a, b, c \in \mathbb{R}. I tried to get this from |a-b| \leq |a-c|+|c-b|, \forall a, b, c \in \mathbb{R}, but I couldn't succeed. Thank you.

Homework Statement Suppose T is an equilateral triangle on the sphere of radius R = 1. Let \alpha denote the angle at any of the three vertices’s of the triangle. (Recall that 3\alpha > n.) Use the result of the last problem on the previous homework and the inclusion - exclusion principle...

1. Three charges are at the corners of an isosceles triangle as shown in the figure. The +q1 = 5.05 uC and -q1 = 5.05 uC charges form a dipole. A) Find the magnitude and direction of the net force that the q2 = 8.50 uc charge exerts on the diple. B) For an axis perpendicular to the line...

I've been reading that the center of mass of a right triangle - the coordinates of the COM, is (1/3b,1/3h)- I can't for the life of me figure out why this is. Is there some sort of clear proof I can take a look at? I don't really know what to integrate..

Homework Statement Use the given information to determine the area of each triangle. Two of the sides are 5cm and 7cm, and the angle between those sides is 120 degrees. Homework Equations Trig functions The Attempt at a Solution I tried drawing up a picture but it's of no help...

Triangle ABC has side-lengths AB=12,BC=24,and AC=18. The line through the incenter of ABC parallel to BC intersects AB at M and AC at N. What is the perimeter of triangle AMN? (A)27 (B)30 (C)33 (D)36 (E)42 My friend is saying my solution is too messy and there was no need for the heron's...

Homework Statement So I have several problems on my homework which deal with the application of cross product and its magnitude to find areas. I know how to do cross product, and I know how to find the magnitude, however, no matter how many times I try to calculate it, I get the wrong...

I am familiar with the proof for the following variant of the triangle inequality: |x+y| ≤ |x|+|y| However, I do not understand the process of proving that there is an equivalent inequality for an arbitrary number of terms, in the following fashion: |x_1+x_2+...+x_n| ≤...

The triangle inequality states that, the sum of any two sides of a triangle must be greater than the third side of the triangle. But the triangle law of vector addition states that if we can represent two vectors as the two sides of a triangle in one order ,the third side of the triangle...

I was watching a Horizon program the other night on the BBC and was interested that they were able to repeat the "triangle on the surface of a sphere" experiment on the universe as a whole. When this experiment is performed on the surface of the Earth on a large enough scale the angles of...

Homework Statement The altitude perpendicular to the hypotenuse of a right triangle is 12 cm. Express the length of the hypotenuse as a function of the perimeter. Homework Equations The Attempt at a SolutionSo I have to express the hypotenuse (h) in terms of the perimeter. I tried to find the...

Imagine a light source, double-slit, and a curved screen in vacuum, shaped so that all parts of the interference pattern are created simultaneously. Define distance as proportional to the time light requires to reach a point. Detectors at each slit can be operating or not. Call the source S...

Looking at maps of the age of the seafloor, one can see a rough triangle in the Pacific near the Marianas Trench that represents the oldest area of the Pacific plate. Some maps mark the very oldest area as being roughly at the centre of this triangle. Upon seeing this I found myself asking how a...

Homework Statement Show that |x_1 + x_2 + · · · + x_n | ≤ |x_1 | + |x_2 | + · · · + |x_n | for any numbers x_1 , x_2 , . . . , x_n Homework Equations |x_1 + x_2| ≤ |x_1| + |x_2| (Triangle inequality)The Attempt at a Solution I tried using the principle of induction here, but to no avail...

Consider an equilateral triangle of side 15.6cm. A charge of +2.0μC is placed at one vertex and charges -4μC each are placed at the two. Determine the electric field at the centre of the triangle. I used Pythagoreom theory to find the height and divided it by 2 but now I'm stuck because I...

This is a fairly standard maximization problem in calculus, but I was wondering if anybody could help me come up with a nice geometric solution. It seems like it should be possible to make an argument based on symmetry, but I haven't quite been able to work it out yet. Note, I have already...

Homework Statement Prove: If a2+b2=1, and c2+d2=1, then ac+bd ≤1 Homework Equations Maybe triangle inequalities theorem. The Attempt at a Solution

Homework Statement Find the mass of the surface of the triangle with vertices (2,0,0), (0,2,0) and (0,0,1) if the density is 4xz. The solution is attached as TheSolution.jpg. Homework Equations Integration. Cross product. Plane equation: a(x-x_0) + b(y-y_0) + c(z-z_0) = 0 where <a,b,c> = n...

Homework Statement The problem is attached as TheProblem.jpg and the answer is D. Homework Equations Perhaps the equations attached in Metric relationships summary.pdf. The Attempt at a Solution My logic is as follows: For A, XW does not necessarily equal WZ. For B, it seems that...

Homework Statement Having a bit of trouble with this one, specifically the answer of (ii) (Q. diagram included as attachment). Can anyone help? Many thanks. Q. In the given diagram, the angles prq & pqs are both right angles. The \anglerpq = X, \angleqps = Y, |pr| = a & |ps| = b. (i)...

Homework Statement 4 identical charges each equal to Q are placed at the 4 vertices of a regular triangular pyramid of each side equal to 'a'. Find the net electrostatic force on anyone charge. Homework Equations F = kQ^2/a^2 The Attempt at a Solution find the force due to each...

Homework Statement Points are A(-6,2) and B(-3,4) and ellipse 4x^2 + 9y^2 = 72. Point C(x,y) for which triangle ABC has largest area is? Homework Equations Ellipse equations The Attempt at a Solution I don't know even where to start. As far as i am concerned that point can be any...

For part (i), my answer is correct but my answer for (ii) seems to be a little bit out. I can't spot where I've gone wrong. Can anyone help me out? Many thanks. Homework Statement Q. In the given triangle, find (i) |\angle abc|, (ii) |\angle bac|. The Attempt at a Solution (i) cos B =...

Homework Statement These are really frustrating because they seem so simple, I work them all out without a hitch only to find that I'm wrong half the time and left wondering why. In fig 21-26a, particles 1 and 2 have charge 20 microcoulombs each and are held at separation distance d = 1.5...

Homework Statement the tangent of the graph 1/x^2 at P(2,1/4) forms a triangle with the x and y axis. Find area of triangle.Homework Equations The Attempt at a Solution so f'(x)=-2/x^3 so the slope of the tangent at point 2, is f'(2)=-2/8 = -1/4=mt now i use the equation of the line to...

Homework Statement (I don't know how to draw a picture here so I will just explain the dimensions of the similar triangles) A lightbulb on a floor shines at a 2m tall guy who is walking away from it towards a wall. As he gets closer to the wall, his shadow gets smaller and smaller on the...

Homework Statement A circle is inscribed in a triangleHere is a picture Picture of circle inscribed in triangle, not necessarily to scaleWhich is larger: the circumference of the circle, or the perimeter of the triangle? Homework EquationsC=∏D (D=diameter of the circle, C=circumference of...

A (51) D E (42) C (56) H (56) B Isosceles triangle ABC, AB = AC, base BC = 112. D is on AC: line BD crosses height line AH at...

[FONT=arial]thanks.. an explanation on how to do it will help!1.Can a triangle have angles equal to a. 55[FONT=arial]°, 65[FONT=arial]°, 70[FONT=arial]° b. 53[FONT=arial]°, 64[FONT=arial]°, 73[FONT=arial]° c. 80[FONT=arial]°, 105[FONT=arial]°, 5[FONT=arial]° [FONT=arial] 2. In...

Homework Statement An equilateral triangle of side x is is inscribed in a circle. Express the area of the circle as a function of x. Homework Equations Anything non-trig. I suspect it's got something to do with the Pythagorean theorem. The Attempt at a Solution I tried getting the...

Here is what I got so far: But the solution 15.7875 MPH is incorrect so undoubtedly my angle would come out incorrect too. Where have I gone wrong?

(Plse bear with me: until i learn how to fly this thing, / must stand for radical) If the side ratio for a 30:40:90 deg right triangle are 1 : /3 : 2 then, is the following true: one may multiply this ratio by 1,2,3 or 5,6,7,8,9 or 10 and the pythagorean identity obtains but NOT by 4 If so...

Homework Statement The two sides lengths of a triangle is exponentially distributed. (not so important for my question) The angle between the sides is uniformly distributed [0,2∏] c) explain why the probability to get obtuse triangle is greater then 0.5 The Attempt at a Solution...

Homework Statement B(-6,-7,-3) C(2,7,3) D(-4,-1,-11) Find the equations of the plane containing the triangle BCD. The attempt at a solution I've gotten to the end and got an equation, but the normal vector it has is just making me really paranoid. Vector BC = [2+6, 7+7, 3+3] =...

Hi i have a right angle tringle, base=1200m and h=400. I have trouble understanding on how to determine the centroid i know one side will be 2/3*x and another side would be 1/3*y. But i don't understand how to write it out. A friend said its 1/3*1200*400*2/3*1200, but i have no idea and...

An angle -- why an angle is the ratio of two sides of a triangle? Perhaps I should have already learned this, but I just can't seem to grasp why an angle is the ratio of two sides of a triangle, or the length of a circular arc by its radius.Why is this so?

Homework Statement In triangle ABC, the median from C meets AB at D. Through M, the midpoint of CD, line AM is drawn meeting CB at P. If CP=4, find CB. Homework Equations The Attempt at a Solution I constructed this drawing on GSP and found CB to be 12. I'm trying to show...

Hi everyone, I have a question on Rudin's proof of Theorem 1.33 part e. Here he prove the following statement: The absolute value of z+w is equal or smaller than the absolute value of z plus the absolute value of w -Yes, is the triangle inequality, where z and w are both complex numbers-...

I know the following |x|-|y| \leq |x+y| \leq |x| + |y| where does |x-y| fit in the above equation?