Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [triangles]

For questions about properties and applications of triangles.

A triangle is a polygon with three sides. It is an important geometric figure, because any polygon can be subdivided into triangles.

Triangles can be classified by the number of sides they have that have equal length

  • All three sides of an equilateral triangle have equal length.
  • An isosceles triangle has at least two sides of equal length.
  • A scalene triangle is a triangle that is not isosceles, that is, it has no sides with equal length.

A triangle may also be classified by describing its angles. A triangle is said to be a right triangle if it contains a right angle, and obtuse triangle if it contains an obtuse angle, or an acute triangle if all three of its angles are acute.

6703 questions
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A triangle has sides $2n, n^2+1$ and $n^2-1$ prove that it is right angled

I've tried using Pythagoras theorem but it always results in a silly answer like $n=n^2$ or something. I'm nearly 100% sure this is done with Pythagoras but I'm not sure which way to do it
Tommy101
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Finding the lengths of this triangle?

please help, i'm to answer the question. The length of AB is 14.67106m. Please give working outs.
Inkaho
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Vectors: right triangle, two vertex known and a direction vector parallel to unknown point

The endpoints of the hypotenuse of a right triangle ABC are A(-10,10,9) and B(14,0,-4). The point C lies on the line that passes through the point A and is parallel to the vector 2i-2j-k. Determine the coordinates of the point C.
Eliisa
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Bounding inradius, given circumradius.

The problem in my book is as follow. In a $\Delta ABC$ , if $r=r_2+r_3-r_1$ and $\angle A >\dfrac{\pi}{3}$ , then the range of $\dfrac{s}{a}$ is equal to: (Here $r_i $ are exradii) I used the fact that $r_1+r_2+r_3=4R+r$ , to arrive at…
Someone
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Right Triangle Theorem/terminology

Given a line segment $s$, there are exactly two right triangles which have $s$ as a hypotenuse. Is there a name for this theorem? Assuming this line segment lies on a Cartesian plane, how can we compute the points at which the legs of these two…
Isaac Kleinman
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Relationships in a triangle

Here is the question, I can''t figure out how to explain this algebraically.
joe
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using slope to find an angle in right angled triangle

I have a right angled triangle in which I know the length and the slope of the hypotenuse, how do I find one of the angles? Thanks
Jerry Murphy
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In this figure find AC=x

Can you find $AC$, when only the angle $DBC$ and $DEB$ are $90$ grades. I can't because I think they should give the angle $CAB=90$ grades too.
user195144
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30 60 90 Triangle question.

A right triangle has a hypotenuse of $\sqrt{10}$, one of the legs is $x+2$, and the shortest leg is $x$. How do I find $x$? Thanks.
David
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Choosing the angle in rectangular coordinates

Find all possible polar coordinates for the point P that has rectangular coordinates ( -2,2 (3)^(1/2) ). At the end, the equation satisfied by which angle ? How to know it ? The cos angle or the sin angle ?
MuhammadJ
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Which of the following are the correct angle measures for angles 1 and 2 in the triangle shown below?

http://www.explorelearning.com/ELContent/gizmos/ELMath_Deliverable/ExplorationGuides/Geometry/images/EL_GEO_TriSum6.gif A. mangle1 = 43°, mangle2 = 137° B. mangle1 = 137°, mangle2 = 43° C. mangle1 = 43°, mangle2 = 47° D. mangle1 = 79°, mangle2 =…
laurent dormeus
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Two triangles with two equal sides and equal area will have the third size also equal?

Consider two triangles $\triangle abc$ and $\triangle def$ such that $ab=de$ and $ac=df$.Also area of $\triangle abc$ is equal to area of $\triangle def$.Now draw $cm$ perpendicular to $ab$ and $fn$ perpendicular to $de$.$ab$ and $de$ are equal and…
user3311810
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Proving the following inequality in a triangle

In a triangle the straight lines $AD$, $BE$, $CF$ are drawn through a point $P$ to meet $BC$, $CA$, $AB$ at $D$, $E$, $F$ respectively: Prove that $$\frac{PD}{AD} + \frac{PE}{BE}+\frac{PF}{CF}=1$$ and $$\frac{AP}{AD}+…
Apoorv Jain
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Prove that $\sin A - \sin B + \sin C = 4\sin A/2 \cos B/2 \sin C/2$

Prove that $\sin A - \sin B + \sin C = 4\sin A/2 \cos B/2 \sin C/2$ occurs in an $ABC$ triangle. I don't know how to solve the RHS... Can anyone help me please?
user3018347
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If an equilateral triangle has an area of 36 units squared, what is the length of a side to the nearest tenth?

I have been working with finding the area of a regular triangles, squares, and hexagons using special right triangle formulas drawn from the radii and apothems, but I cannot for the life of me work backwards. How would I find a side length given the…
Matthew
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