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.

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Calculate points of parallel plane?

If I have $3$ points $(x,y,z)$ that define a plane and want a parallel plane with the same amount of points, just offset by $2$ units, what would be a good start point regarding the math/algorithm?
Robert Fisher
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Trigonometry problem, using COS

Let's say two right angled triangles share a common hypotenuse which measures 10 in length and share an angle which measures $20^\circ$ in total. How do I work out the value of x (the side adjacent to the $20^\circ$ angle)? Using $\cos$ looks like…
jaykirby
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is there a formula for working out the angles of a triangle to make the sides meet at the top?

I am doing a GCSE maths foundation paper for revision and one question has a triangle with the base side being 9cm and the other 2 sides 7.5cm. Is there a formula for finding the angles of the triangle given the lengths of each side so that the 2…
crmepham
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Is it possible to find the length of two sides of a right angled triangle with only one number given.

I was doing my math homework when I got a question that asked as follows: The area of a square drawn on the hypotenuse of a isosceles triangle is 24cm2. Find the lengths of the other two sides, $b$ and $c$. Even though you only have one number…
Mr Jury
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How to get the coordinate of the 3rd side of a triangle if you know the length of all sides and the coordinate of other two sides

I have seen similar questions before but there most of the part is that in general they start from origin.But here is my question. Just in a plane you have to construct triangle at some random place.The values of (x1,y1) and (x2,y2) are known and…
chethanv77777
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How do I obtain the inequality for the two points of a triangle that fullfill a condition?

This problem states that on $△ABC$, $AB=3$, $AC=1$, $AD=1$ $∠BAC=θ$. It says that there are two points that fullfill the condition $DP_0=\frac{1}{3}BC$ and asks for the range of $\cos \theta$ that is needed to fullfill the condition. These images…
ラゴズ
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comparisons of side lengths on a triangle

I am trying to find the relationship between the sides of any triangle as part of a bigger problem. I was thinking about altering the Pythagorean theorem, but all I got was the useless $a^2+b^2\lesseqgtr c^2$ which is basically completely…
Arale
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In a triangle is there an angle splitter formula like angle bisector theorem but generalized?

A segment starting from a vertex of a triangle splits that angle in 2 arbitrary parts. It also splits the opposite triangle side in 2 parts. Can a relationship be established between the angle parts and the side parts, like the proportional…
mireazma
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How do I go about calculating the perimeter of a triangle that consists of three vertices of a cube?

I'm given a unit cube. The task is to find the perimeter of triangle ACE. I have no other information, but considering it's a unit cube that should be more than enough. Am I looking for an answer like this by any chance? Anyways, cheers!
Bobbbay
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How to find out length of bisector?

I found this challenge online but can't solve it. I have a triangle C is 90 degrees. The bisector of A cuts BC into 5 and 3, how do i find out how long the bisector is?
Mohammedhamed46534
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How to find the shaded area of a triangle formed by the tangent of a circle?

Hey guys, The last question of the chapter has stumped me once again! I need to find the area of part of this triangle. I’m not sure how to attack the question considering that I’m not given the radius of the circle and I’m not sure how the…
Scratch Cat
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Let $p,q,r$ denote sides $QR, PR, PQ$ of $\Delta PQR$ respectively. Then prove that $p\cos^2 (R/2) +r \cos^2 (P/2) = \frac{p+q+r}{2}$

Let $p,q,r$ denote sides $QR, PR, PQ$ of $\Delta PQR$ respectively. Then prove that $p\cos^2 (R/2) +r \cos^2 (P/2) = \frac{p+q+r}{2}$ Can I get a hint so that I can get started? I tried using the standard half angle formula, but they don’t work.
Aditya
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Analize given data about a triangle PQR and solve

In a non right triangle $PQR$, the median from $R$ meets the sides $PQ$ at $S$, the perpendicular from $P$ meets sides $QR$ at $E$ and $RS$ and $PE$ intersect at $O$. $p=\sqrt 3, q=1$ and circumradius of $PQR$ is $1$. I don’t want the complete…
Aditya
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If in a Triangle ABC b , c , B ( where A ,B ,C denotes angles and a , b ,c denotes sides of the triangle ABC ) are given and b < c . Prove that

If in a Triangle ABC b , c , B ( where A ,B ,C denotes angles and a,b,c denotes sides of the triangle ABC ) are given and b < c prove that $$ \ sin \frac {(A_1-A_2)} {2}\ = \frac { (a_1-a_2)} {(2b)} $$ MY ATTEMPT : taking cosine rule $$…
victor
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find area of Triangle ABF

In the figure given below, rectangle $CDEF$ with perimeter $32$ has the maximum area. Find the area of the triangle $ABF$ So, I tried the following $P = 2W+2H$ where $P$ is given $32$. I am not able figure out which will be next step & how can I…
SSK
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