A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted
△
A
B
C
{\displaystyle \triangle ABC}
.In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane (i.e. a two-dimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is only one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is no longer true. This article is about triangles in Euclidean geometry, and in particular, the Euclidean plane, except where otherwise noted.
Here is my attempt to draw a diagram for this problem:
I'm confused about the "the perpendicular bisector of ##BC## cuts ##BA##, ##CA## produced at ##P, \ Q##" part of the problem.
How does perpendicular bisector of ##BC## cut the side ##CA##?
Summary:: I think we are still in the earlier parts of Physics and I am confused at how "values" work for a velocity-time graph. We are using the formulas to solve an area of a triangle and rectangle to find the total displacement. If a diagonal line begins from above and continue to go down...
Reading The Theoretical Minimum by Susskind and Friedman. They state the following...
$$\left|X\right|=\sqrt {\langle X|X \rangle}\\
\left|Y\right|=\sqrt {\langle Y|Y \rangle}\\
\left|X+Y\right|=\sqrt {\left({\left<X\right|+\left<Y\right|}\right)\left({\left|X\right>+\left|Y\right>}\right)}$$...
##AD## is diameter, thus ##\angle ACD = \angle ABD = 90^\circ##. Also ##HBDC## is a parallelogram because ##HC||BD, HB||CD##. It seems useless and I don't know how to continue. Thank you in advance!
Homework Statement
Points E and F are the focuses of the hyperbola and point X are on the hyperbola. Determine the size of the main and minor half-axes of the hyperbola.
Homework Equations
x2 = e2 - f2
x = 8
The Attempt at a Solution
I think that eccentricity is 4 units (x/2). But I don’t...
1. The problem statement, all variables, and given/known data
Triangle ABC has a point D on the line segment AB which cuts the segment in ratio AD : DB = 2 : 1.
Another point E is on the line segment BC, cutting it in ratio BE : EC = 1 : 4.
Point F is the intersection of the line segments AE and...
Homework Statement
Homework Equations
d(y)/d(x) --> max area
area of triangle = 1/2 . base . height
The Attempt at a Solution
for number (2) [/B]
x^2 + y^2 = r^2 --> circle equation
base = 2R, height = y
Area = 1/2 . 2R . y
area = 1/2 . 4. √ (r^2 - x^2)
area now is half of max = 2...
1. Find α(β) given that the sum of the 2 sides= ##(x+y)## and its third, ##z## is a constant for 0<β<180.
You can imagine that there's two pieces of string connected between two points. One string is as long as the distance between the two points while the other string is longer. If you...
Determine the area of the painted hexagon, knowing that the area of triangle ABC is 120cm^2
IMG Link: https://m.imgur.com/a/WtdsW
I tried using Heron´s formula, but just ended up with a bunch of terms and one more variable.
Sidenote: I guess part of it is figuring out that the side lenghts...
Homework Statement
Suppose you have a Triangle with the vertices, (0,0) (1,1) and (0,1). Integrating along that path.
I have some differential function dZ where Z = Z(x,y)
Homework Equations
The Attempt at a Solution
[/B]
If I need to integrate, then I need to find the limits of...
Homework Statement
In the drawing you can see a circumference inscribed in the triangle ABC (See the picture in the following link). Calculate the value of X
https://goo.gl/photos/CAacV2dJbUrywfXv9
2. The attempt at a solution
It seems I found a solution for this exercise with the help of...
The statement:
In every ABC triangle, the laws of sine (a/sinA = b/sinB = c/sinC) & cosine (c2 = a2 + b2 -2*a*b*cosC) are valid, where a, b & c are the sides opposite to A, B & C respectively.
Write a program that calculates and prints on the computer's screen, the length of c, and also the...
Homework Statement
Find the expression for the electric field at point M(a,a,0) if the linear charge density is known ( ##Q'## )
Homework Equations
3. The Attempt at a Solution [/B]
I tried something like this and would like your feedback on it. I separated the triangle into three parts...
Homework Statement
The three vectors A, B, and C point from the origin O to the three corners of a triangle. Show that the area of the triangle is given by 1/2|(BxC)+(CxA)+(AxB)|.
Homework Equations
The Attempt at a Solution
I know that the magnitude of the cross product of any two vectors...
Homework Statement
Let P be a point on the sphere with center O, the origin, diameter AB, and radius r. Prove the triangle APB is a right triangle
Homework Equations
|AB|^2 = |AP|^2 + |PB|^2
|AB}^2 = 4r^2
The Attempt at a Solution
Not sure if showing the above equations are true is the...
So I am working on this simple proof, but am confused about the term "external angle." The problem says that if ##a##, ##b##, and ##c## are external angles to a triangle, then ##a + b + c = 360##. However, is seems that the vertex of each triangle has two possible external angles, since there...
<<Mentor note: Missing template due to originally being posted elsewhere>>
Hello everyone.
I have the following problem:
Determine the angles of a triangle where two sides of a triangle are formed by the vectors
A = 3i -4j -k and B=4i -j + 3k
I thought that I would find the third side being...
Hello! I am currently in Calculus 2 and we are dealing with hydrostatic force. I get the integration that happens but I always seem to have trouble with solving the word problems. With this problem, I realize that I use integrate by making an infinite number of rectangles on the 2 triangles. I...
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...
1. Homework Statement
Find forces P,F,and T
Homework Equations
Fx = 0
Fy = 0
The Attempt at a Solution
So far I only got force T from getting the moment from point b. Don't know how-to start getting force P and F since they're both at the same point. Any help will be much obliged thank...
Homework Statement
Two lines passing through a point Μ are tangent to a circle at the points A and B. Through a point С taken on the smaller of the arcs AB, a third tangent is drawn up to its intersection points D and Ε with MA and MB respectively. Prove that (1) the perimeter of ▲DME, and (2)...
Homework Statement
As shown in the diagram below, the shape consists of a square and a circle with centre Q. Given that QM = 3 cm, prove that MN = 6 cm.
Known data:
-- triangles APB and BQC are congruent
-- angle BMC = 90
-- triangles BMQ and BNA are similar and right-angled
2. Homework...
Homework Statement
Triangle ABC have side AB = 10 cm, AC=BC = 13cm, so sin (A-C) is...
2. Homework Equations
sin (A-C) = sin A cos C - cos A sin C
The Attempt at a Solution
I see that the triangle can be split into two right-angle triangles.
But, sin (A-C) ?? How to get that?[/B]
How can I get a right triangle from the inputs and outputs of trigonometric functions?
For example: sin(x) = y
The triangle would have one angle as x and the opposite edge of the triangle would be y/hyp etc.
How can I get all of these values from any trigonometric function?
Please tell me if I...
The problem
A right triangle has an angle a and we know that ##cos \ a = \frac{1}{3}##. What is ## tan \ (90°-a) ##
The attempt
I know that the ration between the adjacent side and the hypothenuse is 1/3. I am not interested in the real lengths of the sides.
I can therefore calculate the...
This is supposed to be a simple question. However, I forgot a lot of the basics and rules I have to follow.
I tried to workout the height based on the area:
0.5 x 3 x h = 30
h = 20
But couldn't figure out the rest.
Then I thought about going by ratio (not from knowledge but out of...
Hey Guys. I'm having a bit of a problem with my solving triangles book. I'm finding the book really easy but there's this one thing that I keep getting wrong. Whenever I'm working with degrees with decimal points my answer aways fluctuates slightly from the real answer. I must be doing something...