# Questions tagged [triangle]

For questions about properties and applications of triangles.

3,913 questions
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### Calculating the annulus of a sphere with a differential change in theta

Consider the following object: I want to calculate the area of the annulus. The annulus is within the region of $$\theta$$ and $$\theta + d\theta$$ The answer of the area of the annulus is ...
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### Fourier Series of Triangular waveform

Fourier Series of Triangular waveform this is the solution of Fourier series of a triangular waveform from the book Circuits and Networks: Analysis and Synthesis by Shyammohan S. Palli. In this ...
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### Prove that $\frac{BC}{AH}×\frac{CA}{BH}×\frac{AB}{CH}$ = $\frac{BC}{AH}+\frac{CA}{BH}+\frac{AB}{CH}$, where $H$ is the orthocenter of $\triangle ABC$

It is an isolated problem which has a lack of context. I found that problem in a magazine which was stated such as below: In $\triangle ABC$, three altitude lines $AE$, $BF$ and $CD$ dropped from ...
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### Show that no matter how $12$ points are put on a plane, there are $3$ among them forming an angle not greater than $18^o$.

Problem : Show that no matter how $12$ points are put on a plane, there are $3$ among them forming an angle not greater than $18^o$. I am not getting any ideas in solving this problem. So, there ...
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### Trigonometry right angled triangle bearing question [closed]

I don’t know how to do part b of question 16 from the picture that I have inserted, please insert a clear explanation as well. The answer on the book is 66 degrees. Thank you!
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### Spherical triangles and congruence criteria

I read from different sources that the usual criteria of congruence of triangles work for spherical triangles. However it seems to me that there is a counterexample. Consider two poles on the sphere A ...
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### What is the value of $x+y$ if x and y are co-primes and $PR=\dfrac{x}{y}$ in the diagram?

$ST$ is the perpendicular bisector of $PR$ and $SP$ is the angle bisector of $\angle QPR$. If $QS=9cm$ and $SR=7cm$ then $PR=\dfrac{x}{y}$ where x, y are co-primes. $x+y$=? Source: Bangladesh ...
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### Find the $\angle ACB$ of $\triangle ABC$.
If $PC=2BP$, $\angle ABC= 45^\circ$, and $\angle APC=60^\circ$, find $\angle ACB$. All solutions are acceptable but please try solving using reflection of point $C$ through the line segment $AP$. I ...