Triangle Definition and 1000 Threads

Given that triangle $ABC$ is congruent to triangle $CDE$, and that $\angle A=\angle B=80^{\circ}$. Suppose that $AC=1$ and $$DG=\frac{2\sin 10^{\circ}}{M+N\sin^2 10^{\circ}}$$. Evaluate $M+N$. [FONT=serif].

hopefully this is the right place for this question, the first part is a trig/geometry question but it is really a integration question: i'm trying to find another way to compute d1 without using law of cosines because i don't know how to integrate (cos a)^.5, if someone knows how to do that...

Math Problem: Find the length of the third side of a triangle if the area of the triangle is 18 and two of its sides have lengths of 5 and 10. Which one of these are correct when I am working them out? If none of these are correct, then can somebody please help me solve this math problem...

Hello all, I am currently reading about the triangle inequality, from this article http://people.sju.edu/~pklingsb/cs.triang.pdf I am curious, how does the equality transform into an inequality? Does it take on this change because one takes the absolute value of 2uv? Because before the...

A triangle PQR has the following property: There is an interior point $A$ such that $\angle APQ=10^{\circ}$, $\angle AQP=20^{\circ}$, $\angle ARP=30^{\circ}$ and $\angle APR=40^{\circ}$. Prove that the triangle PQR is isosceles.

Homework Statement As ship is anchor off a long straight shoreline that runs north and south. From twi observation points. 15 miles apart on shore the bearings of the ship are N 31 ° E and S 53 ° E. What is the shortest distance from the ship to the shore. Homework Equations Sin θ Opp/...

I have the expression $$sin^{-1}(cosx)$$ I'm not sure how to simplify this at all. I've never done a problem like this and it's in my textbook as a review question. A quick boot in the right direction would help

How do I find the volume of this shape? The bottom is a square in the xy plane where \(0\leq x,y\leq 1\). The object isn't a prism or pyramid so I am not sure what to do.

Homework Statement Three point charges have equal magnitudes, two being positive and one negative. These charges are fixed to the corners of an equilateral triangle. The magnitude of each of the charges is 2.9 µC. The lengths of the sides of the triangle are .02m Calculate the magnitude...

Homework Statement Uploaded Homework Equations Uploaded The Attempt at a Solution I actually need someone to check my work for 1.1 and 1.2. Is what I have done in 1.3 correct I mean it does not seem right?

Hi there, the problem says, an n-gon is circumscribed around a circle so the mid point of each side is tangent to the circle. Prove the triangle consisting of one side of the n-gon and the sides from the end points to the middle of the circle has area tan(pi/n) Cheers!

this is best I can figure for the triangle (shaded) but $$\vec{OC}$$ looks like it has decimals in it.

P is an inner point of equilateral triangle ABC , given PC=3, PA=4,PB=5 ,please find the side length of the equilateral triangle

Consider the isosceles triangle circumscribed about the ellipse: Find the altitude of the triangle when its area is minimized.

Homework Statement I'm trying to express the function of a equilateral triangle as a function of the length of a side. All you know is the sides are all equal Homework Equations I have the answer but i don't understand (how and why they got there) and they used the A of a triangle as A=...

Homework Statement Let a be a unit vector and b be a non-zero vector not parallel to a. Find the angles of the triangle, whose two sides are represented by the vectors √3(a x b) and b-(a.b)a Homework Equations The Attempt at a Solution The third side will be equal to \sqrt{3}(a \times...

$\triangle ABC , \angle ABC=45^o,\,\, point \,\, D\,\, on \,\, \,\overline{BC} $ $and,\,\, 2\overline{BD}=\overline{CD},\,\, \angle DAB=15^o$ $find :\,\, \angle ACB=?$

Homework Statement I'm trying to solve the following problem : In △ABC, coordinates of B are (−3,3). Equation of the perpendicular bisector of side AB is 2x+y−7=0. Equation of the perpendicular bisector of side BC is 3x−y−3=0. Mid point of side AC is E(11/2,7/2). Find AC2. Homework...

Homework Statement Hi, I have inserted a picture of the problem: I have to find x, the altitude, or height of the triangle. x is the height of the larger triangle, and is perpendicular to the base of 13. It divides the base into segments of length 4 and 9. This was a question on...

Would this would the proper function, as described in the title of this thread, A = 1/2 x^2 \cos \frac{\theta}{2}? And suppose that the side x and the angle were changing with time, would the derivative, with respect to time, be \frac{dA}{dt} = x \cos \frac{\theta}{2} - 1/4 x^2 \sin...

Homework Statement The following is a geometry question I can't seem to get. "Consider an acute angle △ABC. Points D, E, F are mid points of sides BC, CA and AB respectively. G is the centroid of △ABC. Area of △AFG = 14, EC = 15/2. Perpendicular distance of F from BC = 6. Find BC2−AB2 "...

Please see the image attached. Does that have anything to do with directions? The right-hand rule?

Triangle ABC has $$AB=9$$ and $$BC:AC=40:41$$. What's the largest area that this triangle can have?

Homework Statement Taken from Spivak's Calculus, Prologue Chapter, P.28 b) Notice that all numbers in Pascal's Triangle are natural numbers, use part (a) to prove by induction that ##\binom{n}{k}## is always a natural number. (Your proof by induction will be be summed up by Pascal's...

Homework Statement An 800 g steel plate has the shape of the isosceles triangle shown in the figure. What are the x and y coordinates of the center of mass? https://www.physicsforums.com/attachment.php?attachmentid=13559&d=1208292919 Homework Equations x=1/M ∫ x dm [b]3. The...

I'm beginning to read Spivak's Calculus 3ed, and everything is smooth until I reach page 12. My question is marked, between line 2 and 3. Why there's such sign change suddenly? In fact I tried with simple line 4 case and it's not in fact equal. I'm assuming that a and b is valid for all...

[FONT=times new roman]the following diagram shows a circle with center $$O$$ and a radius $$4cm$$ The points $$A, B,$$ and $$C$$ Lie on the circle. The point $$D$$ is outside the circle, on $$(OC)$$ Angle $$ADC=0.3$$ radians and angle $$AOC=0.8$$ radians (a) find $$AD$$ I used law of...

ABCDE is a pentagon,now please construct a triangle APQ ,and both of them must have the same area

Physical Problem -- triangle as a pool table Hello, can you please help me? It is an irregular triangle as a pool table: At point A, there is a small billiard ball. How should the bullet hit, that it hits first the band 1, then 2, and finally with the band 3, after a shock again arrives...

In a group of $$n$$ people, each pair are friends or strangers. No set of three people are mutually friends. For any partition of the $$n$$ people into two groups, there exists two people in a group that are friends. Prove that there exists a person who is friends with at most $$2n/5$$ people in...

Hello MHB, I am working with an old exam that I don't get same answer. Line $$l_1(x,y,z)=(1,0,1)+t(2,-1,-2)$$ and $$l_2(x,y,z)=(2,-5,0)+s(-1,2,1)$$ intercept on point A also interpect on plane $$\pi:-x+2y-z+4=0$$ in point B and C, decide area of triangle ABC Progress: Point A: If we equal them...

Hi all, How would you determine the angle i in the following equilateral triangle. Thank you.

You have a thin rod of length $\ell$ and you cut it randomly into three pieces. Calculate the probability that the three pieces can form a triangle.

Homework Statement Use the triangle inequality to prove that \left| s_n - s \right| < 1 \implies \left| s_n \right| < \left| s \right| +1 Homework Equations The triangle inequality states that \left| a-b \right| \leq \left| a-c \right| + \left| c-b \right| The Attempt at a Solution...

Homework Statement In a ##\Delta ABC##, angle A is greater than angle B. If the measures of A and B satisfy the equation ##3\sin x-4\sin^3 x-0.75=0##, then angle C is equal to A)##\pi/3## B)##\pi/2## C)##2\pi/3## D)##5\pi/6## Homework Equations The Attempt at a Solution The...

Let ABC is an acute angled triangle with orthocentre H. D, E, F are feet of perpendicular from A, B, C on opposite sides. Let R is circumradius of ΔABC. Given AH.BH.CH = 3 and (AH)2 + (BH)2 + (CH)2 = 7, answer the following Q1. \frac{\prod \cos A}{\sum \cos^{2}A}Q2. What is the value of R...

Hello! I got a problem wrong and I'm trying to figure out what happened. it's triangle ABC bisected by line BD Given line BD is the perpendicular bisector of line AC, Prove line BD bisects angle ABC I got Step 1 Line BD is the perpendicular bisector of line AC Reason: Given Step 2 Line D is...

I recently discovered that for a 3rd degree polynomial I was studying, f(5) - 4f(4) + 6f(3) - 4f(2) + f(1) = 0. At first I just though it was coincidental that the coefficients were the 5th row of Pascal's Triangle, but then I tried a 2nd degree polynomial and found that f(4) - 3f(3) + 3f(2) -...

A, a'...a''? im in the process of typing out an idea I had about triangles, and I wanted some input, but I ran into a problem when I realized I do not know how to denote multiple "prime" angles. In this diagram, I am working with the corners of a triangle, but have extended the rays outwards...

I have found a way to find right triangles using only one side. How do I show you without being deleted?

Someone please help me with this question. I can't do and I have a calculus exam in the morning.

Homework Statement See attachment Homework Equations The Attempt at a Solution If the y-coordinate of the center of mass is given by (1/A)*∫y dA, how come the solution uses bh/2 as the area? This triangle isn't right angled so that area formula should not hold. What am I missing?

Homework Statement Question is attached. I know there's a few ways to solve this, but I'm wondering specifically why my integral of F ds isn't working. Homework Equations F = k * q^2 / r^2 U = ∫ F ds cos 30 = √3/2 s= rcos30 The Attempt at a Solution U = 2 * cos 30 * k *...

Here is the question: http://i259.photobucket.com/albums/hh299/the-real-guitar-hero/Capture_zpsf2b9cd28.png part A = 3√5 b=y=2X+1 c=(0,1) D is where I am confused. Area of triangle = (base x height)/2 from working out, line 2 cuts the x-axis at -1/2. line 1 cuts the x at 7. the height is 3...

In an orthogonal cordinate system determine the area of the triangle with vertices in $$(-4,1)$$, $$(1,4)$$ and $$(-5,10)$$ There is prob many way to solve it so go ahead with your method:) I made a hint for vector method. Hint

considering the set of triangles, whose sides are the x and y axes, and the tangents to the curve $$e^{-5x}, x>0$$ to estimate the maximum area of such a triangle can be. I have no progress, well I know area is $$\frac{x*y}{2}$$.

We know that in triangle ABC angle A equals $$\alpha$$ and side $$a=\frac{b+c}{2}.$$ How to find angles B and C knowing that $$B\geqslant C$$? For which values of $$\alpha$$ the problem has solutions? ps. a, b, c are only notations. answer. $$\frac{\pi-\alpha}{2}\pm\arccos(2\sin\frac{\alpha}{2})$$

Homework Statement See attached image Homework Equations 1/4πε*q/r The Attempt at a Solution I know that since the problem gives centimeters, there are initial changes to units to be made in the permittivity constant. This makes it 8.86x10^-9 N/nanoCoulombs and 100 mm. But...

For the vectors in the figure, with a = 1.1 and b = 2.6, what are (a) the z component of a x b, (b) the z component of a x c, and (c) the z component of b x c? Everything I've tried to look up involves vectors that are in unit notation, etc. I just don't understand how to do it when all you...

I blieve the mid point in space of arbitrary triangle formed by points A,B,C is the point at which the line A -> midpoint(B,C) B -> midpoint (A,C) C ->midpoint (A,B) meet (i also think C is redundant, that where A to mid and B to mid cross is basically the mid point of the whole...