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 Pythagorean problem

We have two points F1, F2. F1-F2 is 21m. We have a point (P) outside the line. The line from F1-P is called D1. The line from F2-P is called D2. P is 12m away from F1-F2 on a straight line crossing F1-F2 in (N) dividing the triangle F1-P-F2 into two…
Arne Morten
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Can two triangles not be congruent but five elements in triangle are same

Can two triangles not be congruent but five elements in triangle are same There are 3 sides and 3 angles in triangle. All 3 sides and 3 angles are collectively called 6 elements
user1228018
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Law of sines on SAS triangles?

Is there any difference between using SSA or SAS for law of sines? Are they the same? For example, assuming Capital letters are angles, opposite legs are lower case If A= 28 degrees, b =14 and c =9(note that we do not know where the leg belong, do…
Harry Iguana
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Discovering measures of a triangle

I'm having trouble studying for an exam with my brother. We are struggling with this exercise: We need to discover all the measures (b,m,h,a). We got a really weird result and we have no means to check if we got it right.
Eduardo Krueger
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What's the minimal length of each side of an equilateral triangle that can get a square of 15 mm inside it?

If I want to know What's the minimal length of each side of an equilateral triangle that can get a square of which each of its sides is 15 mm, inside it (=inside the square)?. How to calculate it? (I'm not looking for the answer, but I'm looking for…
Arithmetic-Enthusiast
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how do I find an angle of an isosceles triangle when it is next to a parallelogram?

$ABCD$ is a parallelogram. $\triangle CDE$ is an isosceles triangle. $\angle DAB \text{ is } 64^°$. Work out the size of the $\angle DEC$.
Jess STAZICKER
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The Integral value of $\lfloor\frac{a}{30}\rfloor$

The altitudes from the angular points $A$, $B$ and $C$ on the opposite sides $BC$, $CA$ and $AB$ of $ABC$ are $210$, $195$ and $182$, respectively. Then what is the the value of $\left\lfloor\frac{a}{30}\right\rfloor$.
user483801
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Find third vertex of triangle on the Cartesian plane

I have a triangle on the cartesian plane where I know the following: $$ A = (x_1,y_1), B = (x_2,y_2), C = (x_3,y_3) $$ I want to find the possible locations for $C$. I know the location of $A$ and $B$. I know that I want the angle $ABC$ will be…
maryfrank
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what is the sine of an isosceles triangle with sides 10^7 and h=1

The angle of an isosceles triangle with sides = 10^7 and h = 1 is according to Wolfram $$ 1.000~000~000~000~000~4 \times 10^{-7} \quad \text{radians} $$ which corresponds to $$ 5.727 \times 10^{-6} \quad \text{degrees} $$ but that values gives the…
user157860
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In $\triangle ABC$ if $C=90^\circ$ then find the value of $1+\sin A-\sin B$

Since $C=90^\circ$ Then $A+B=90$ Take, for instance $A=B=45$ So the origin equation becomes 1 I basically tried inputting the values in every option and arrived at $\frac {r_1}{R}$ Where r is the circumradius and $r_1$ is the radius of the excircle…
Aditya
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Find area of triangle with sides $\sqrt{b^2+a^2}$, $\sqrt{c^2+a^2}$ and $\sqrt{a^2+c^2}$

The sides of a triangle are given by $\sqrt{b^2+a^2}$, $\sqrt{c^2+a^2}$ and $\sqrt{a^2+c^2}$. Please help me in finding the area of the triangle! It'll be in square root with a,b and c
Miles Beckett
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Parallel lines & triangles

Two lines $GE$ and $FD$ meet in $A$. They cut each other at $45$ degrees. Both $G$ and $F$ lie on the circumcircle of square $ALBK$ such that $E$ and $D$ lie on the $KB$ and $LB$ respectively without lying on the corners of the square. I'm supposed…
user574941
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Calculate the third point of an obtuse triangle

I have the x,y coordinates of point A, point B, the distance AB, the distance BC, and the angle at B, which is more than 90 degrees. How do I calculate point C? It's been years since varsity, so my math is very rusty. Please do not assume much :-)
Peet Brits
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Prove that, given a triangle with sides $a,b,c$, there exists a triangle with sides $a+2b,b+2c,c+2a$ that has an area three times the original

Prove that, given a triangle with sides $a,b,c$, there exists a triangle with sides $a+2b,b+2c,c+2a$ that has an area three times the original I have used Heron's formula but got lost in algebra! Any one got other approach?
Callie12
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What is the best way to explain counting triangles

What is the best way to explain such type of questions to 11 years old? and also please let me know the answer as well. Thank you.
Dinesh Potluru
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