Triangle Definition and 1000 Threads

What's the area of the triangle? It's hard because the vertices aren't in the intersections of horizontal and vertical lines, so I have a hard time determining the side lengths, and it's also for Elementary Students Math Olympiads too.

Area of triangle from picture https://en.wikipedia.org/wiki/Special_right_triangle#/media/File:45-45-triangle.svg is ##A_0=\frac{1}{2}##. If that triangle staying still in system S' and S' moving across one of the sides of length ##1## in respect to system ##S## area of the triangle in the...

I do not know where to start. I draw scalene triangle and assign each coordinates to the vertices. Tried writing something but none working. Please give me a hint to start. Thanks

The triangle ABC is a right triangle with A as the right angle and BD is the bisector of angle B. If AB = 12 cm and BC = 15 cm, the length of AD is ... A. 3 cm B. 4 cm C. 5 cm D. 6 cm It was a question for a 9th grader and the book hasn't covered trigonometry by name yet (As in, they don't know...

Point D divides side AC, of triangle ABC, so that |AD|: |DC| = 1:2. Prove that vectors \vec{BD} = 2/3 \vec{BA} + 1/3 \vec{BC}.

The metric for 2-sphere is $$ds^2 = dr^2 + R^2sin(r/R)d\theta^2$$ Is there an equation to describe the area of an triangle by using metric. Note: I know the formulation by using the angles but I am asking for an equation by using only the metric.

I would like to find the triangle ##\bigtriangleup DEF## in the plot below that is inside the right triangle ##\bigtriangleup ABC## given ##\overline{AB}=3, \overline{AC}=4## with ##\overline{BD}=\overline{DE},\overline{AE}=\overline{EF}, \overline{FC}=2\overline{DF}##. However, I'm finding it...

AB=AC. P is on ac such that AP=3PC. Q on CB such that CQ=3BQ. Need to find the length of PQ. I know i can use the Cosine theorem, but the answer is without Cosine.

Hi Guys I need help with this question so if you can help me with the answer please please.

I solve linear equation for getting rotation and position of triangle without rotation and translation matrix. And try it. Just need a AB, BC, AC lenght. Somebody do this before?This is demonstration with camera canon eos 600d. But I don't solve lens distortion yet.

i know its pretty basic but please give some insight for triangle law of vector addition and pythgoras theorem. becuase ofcourse if you use traingle law to find resultant it will be different from what is pythagoras theorem

Hi, I'm trying to work out this question, and the answer I'm coming up with isn't right. Can anyone help me understand the calculation used to work this out?

Hi, Could someone check that I'm right with this one, or put me right! I've worked the value out as x=30 and y (2x) = 60. I've come to this as I think it's an isosceles triangle so the base angles would be equal. Am I right? Thank you!

A parallelogram ABCD has angle A = angle C = 45°. Circle K with the center C intercept the parallelogram through B and D. AD is extended so that it intercepts the circle at E and BE intercepts CD at H. The ratio of the area of triangle BCH and triangle EHD is ... Here I got that triangle BCH...

Hi, I'm trying to work out how I'd calculate the values in the below. Rather than just have the answer, I'd really like to understand how I'd calculate this. Thank you in advance!

Reading The Theoretical Minimum by Susskind and Friedman. They state the following... $$\left|X\right|=\sqrt {\langle X|X \rangle}\\ \left|Y\right|=\sqrt {\langle Y|Y \rangle}\\ \left|X+Y\right|=\sqrt {\left({\left<X\right|+\left<Y\right|}\right)\left({\left|X\right>+\left|Y\right>}\right)}$$...

Two astronauts, Neil and Michael, visit a solid not revolving planet. They mount a jet engine on this planet to get it turning around its axis. Before starting the engine they put three dots on the surface with the help of an isosceles triangle, which measures 1 by 1 meter. Two dots are placed...

##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!

I was trying to find some sort of pattern in the triangle (below) to graph it or find some equation, and I thought maybe measuring something would be a good idea. I was okay just calculating the area for the first few iterations, but then I got confused on how I was supposed to represent like...

Pythagorean triangle ABC with area 8214 has square DEFG with sides = 60 inscribed in it. Side DE of the square lies on the hypotenuse. Find the triangle's side lengths. B E D F C G A

ABC is a triangle. AC=4cm; AB=3cm; A=60 degrees. I need help finding the area of triangle ABC.

I have computed the total length of a 3D triangle and its area. The code is shown below. I want to use file output instead of cout. The file name, cw2task1output, was just given as part of the task, in this case should I make an empty text file named cw2task1output then attach it to the resource...

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...

Homework Statement Let D be the triangle with vetrices ##( 0,0 ) , ( 1,0 )\mbox{ and } ( 0,1 )##. Evaluate the integral : $$\iint_D e^{\frac{y-x}{y+x}}$$ Homework EquationsThe Attempt at a Solution [/B] The answer to this problem is known (...

In an equilateral triangle $ABC$, let $D$ be a point inside the triangle such that $\angle BAD=54^\circ$ and $\angle BCD=48^\circ$. Prove that $\angle DBA=42^\circ$.

For a right isosceles triangle (45-45-90) of hypotenuse 1, solve for the length of the unknown legs. Give an exact answer and rationalize the denominator in the final answer.

Homework Statement https://www.physicsforums.com/threads/find-the-electric-field-in-the-point-p-of-a-right-triangle.965285/#post-6125768 knowing that the three charges are equal and that the angles of the triangle are 90°, 45°, 45°. Homework Equations The Attempt at a Solution I tried...

Homework Statement if the black dot is assumed by (0,0).find the center of mass coordinate of this triangle [/B] i'm sorry but since the pic won't show ill attach the link here https://ibb.co/4Ptw5T7 <Moderator's note: picture added> Homework Equations centroid is 2/3 of median [/B] using...

Homework Statement P(3, 0, 3), Q(−2, 1, 5), R(6, 2, 7) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. (b) Find the area of the triangle PQR Homework Equations A = \frac{1}{2}|\vec{AB}\times\vec{AC}| Source...

LB is bisector of triangle ABC. suppose, there is a new triangle that called AED. alpha is a angle between LB to AD that is bisector of AED. The triangles can be on any place in the plane. What the value biggest angle ($$alpha$$) can be?

Homework Statement Prove that if A,B,C, are the angles of an arbitrary triangle, then m(A)+m(B)+m(C) = 180 degrees by the following method: From any vertex draw the perpendicular to the line of the opposite side. Then use the result already known for right triangles Homework EquationsThe...

Homework Statement ABC is a triangle The angle A = 30 degrees AB = 7cm BC = 5 cm C is an acute angle. Find the size of angle C? Homework Equations I need to use the cosine rule here Cos C = (a^2 + b^2 - c^2) / 2ac The Attempt at a Solution The problem is I do not know the size of side b? So...

Hi there. Can someone tell me how to calculate the length of "a", shown in these drawings? "r" is the radius of the corner, so these 2 sides have the same length. "C" is 90 deg angle "B" is known (the angle of the corner) Here are the diagrams. First example 45 degree corner, second example 75...

Side lengths are a=6, b=6, c=4. Find the area A=1/2*b*h I split the triangle in half to find the height. Since the base is 4, that divided the base into 2: 2^2+h^2=6^2 4+h^2=36 h^2=32 h=4*sqrt(2) =========== 1/2*4*4*sqrt(2)=area of 8*sqrt(2) Did I do this correctly? I do not have an...

Triangle ABC has area 25*sqrt(3). if Angle BAC=30 degrees, find |AC|=|BC|=? the answer I got was 10*4th root(3) Is this correct? I am asking because someone other than my professor wrote the study guid for us for the final and I am not 100% sure what |AC|=|BC| means as my professor never...

what is the area of triangle ABC in the attached? answer is 18 i can not construct any similar triangles here. all i can see is area of ACD is 3 times area of ABD but how does it help me...

Hello, what is the length of x in the attached? I tried the following: of course BE = 5, and also the point D must be the center of internal circle that is tangent to triangle and from there i came up with some equations together with the side ratio formulas of angle bisectors but it didnt...

what is the length x? (FH and HC perpendicular too, which I missed to write) I am totally stuck can not make any progress on this question. Answer should be 5. I don't know how to obtain it

Hello, In the attached, what is the minimum integer value x can take? AD and BD are angle bisectors the answer is 16 - but i do not know how they did it I am totally stuck, could not think of anything here. The angle bisector formula I know does not fit here

Recently I saw this clip on YouTube which has a revolutionary idea of mathematical notations,What do you think about it?

Homework Statement Where is the center of mass of an isoceles triangle? Homework Equations xcm=∫xdV/V (where V is the volume of the triangle) The Attempt at a Solution The representation of the sides is what I'm confused with. Flipping the triangle to it's side is what's recommended to be...

I've attached the problem and my work. When I enter cos^1(6.890625) I get an error, but 6.9 is also not the answer and Does Not Exist is also not an acceptable answer. So where I am going wrong with this?

I was thinking of using Pythagoras here but it didn't get me far Any suggestions?

Homework Statement Determine the triangles where the sides are consecutive elements of a geometric sequence and the angles are consecutive elements of an arithmetic sequence. Homework Equations The Attempt at a Solution I don't really know how to approach this problem, what the solution would...

Consider the spherical triangle $\mathcal{P}$ with vertices $P_1 = (1,0,0)$, $P_2 = (0,1,0)$ and $P_3 = (1/\sqrt{3}, 1/\sqrt{3},1/\sqrt{3})$. Find the angles $\phi_1, \phi_2, \phi_3$ of $\mathcal{P}$ at $P_1, P_2, P_3$ respectively. I know the cosine angles are $\cos(\theta_1) = 0$...

I'm trying to derive these formulas of tributary areas of a slab on beam. The idea is simple.. portions of the rectangle is distributed to the edge by the formulas.. but inside a pure triangle area.. how do you compute for the 2 triangular areas and 2 trapezoidal areas?

A student ask me the question: Why the other angles in Right angle triangle can't be more than 90 degrees? I want to answer him correctly to the question, What Should I Say to Him?

Homework Statement Find the area of a triangle, assume that you don't know the formula of area of any other figure. Homework EquationsThe Attempt at a Solution Well, i was trying to figure out how to find the area of a triangle out of nowhere, but could not get it. I want to know how it was...