# Tagged Questions

For questions about properties and applications of triangles

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### Area of equilateral triangle from circumcircle

I am trying to calculate skewness of triangle. Given the sides of a triangle (not equilateral), I calculated circumradius from which I would like to get area of equilateral triangle.
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### What are the unknown lengths are angles for the roof?

Sharma is building a shed and wants to determine the measurements for the roof. The span of the roof will be 10 feet and she plans to use a 5:12 roof pitch. This means that the roof will rise 5 inches ...
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### Prove $\triangle{ABC}$ is isosceles if $\cos A = \frac{\sin B}{2\sin C}$

In $\triangle{ABC}$, $$\cos A = \frac{\sin B}{2\sin C}$$ How to prove that $\triangle{ABC}$ is isosceles?
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### At what angle does the stone need to be hit?

In curling, it is often necessary to hit and displace an opponent’s stone to win the end. Olivia would like to hit her opponent’s stone with her own stone. If she releases her stone at the hog line, ...
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### Pythagorean theorem expressed without roots in an old Tamilian (Indian) statement

There's an old Tamil statement that predicts the hypotenuse of a right angle triangle to a reasonable level of accuracy considering it doesn't involve roots. This is how it goes: “Odum Neelam ...
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### Find the Vertices of a Triangle from Set of Points

I have a set of cartesian x,y points which I know am fairly certain are on the edges of a triangle. What is the easiest way (either algebraically or algorithmically) to identify what the three ...
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### How do I properly read a clinometer?

If the weight hangs down at roughly 42 degrees, would the angle be 90 degrees - 42 degrees = 48 degrees?
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### What is the unknown angle?

So first off I started with the pythagorean theorem to find the missing leg of the triangle. \begin{align*} 5^2 + b^2 ={}& 8^2 \\ 25 + b^2 ={}& 64 \\ 64 - 25 ={}& 39 \\ \text{missing leg}=...
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### Show that in any triangle, we have $\frac{a\sin A+b\sin B+c\sin C}{a\cos A+b\cos B+c\cos C}=R\left(\frac{a^2+b^2+c^2}{abc}\right),$

Show that in any triangle, we have $$\frac{a\sin A+b\sin B+c\sin C}{a\cos A+b\cos B+c\cos C}=R\left(\frac{a^2+b^2+c^2}{abc}\right),$$ where $R$ is the circumradius of the triangle. Here is my work: ...
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### The inequality $\frac{MA}{BC}+\frac{MB}{CA}+\frac{MC}{AB}\geq \sqrt{3}$

Given a triangle $ABC$, and $M$ is an interior point. Prove that: $\dfrac{MA}{BC}+\dfrac{MB}{CA}+\dfrac{MC}{AB}\geq \sqrt{3}$. When does equality hold?
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### Find the area of triangle, given an angle and the length of the segments cut by the projection of the incenter on the opposite side.

In a triangle $ABC$, one of the angles (say $\widehat{C}$) equals $60^\circ$. Given that the incircle touches the opposite side ($AB$) in a point that splits it in two segments having length $a$ and ...
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### What is the angle of b?

So first off, I know how to find the missing length of the leg of the triangle using the pythagorean theorem. $6^2 + b^2 = c^2$ $36 + b^2 = 100$ $100 - 36 = 64$ $\sqrt{64} = 8$. So angle angle $A$ ...
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### What angle does the board need to be cut at?

If someone has a 2'' wide board and a 1 1/2'' wide board, and they want to cut the narrower board at an angle so the cut is 2'' long and the boards will fit together, what angle do they need to cut ...
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### If a 16' ladder is placed correctly on a level surface, how high up will the ladder reach?

So i have just began learning about sin cos and tan, and i came across this problem and for some reason I'm having trouble figuring it out. *** When using a straight ladder, it is recommended that ...
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### Explain why two right triangles, each with an acute angle of 17 degrees, must be similar.

Two right angles with an acute angle of 17 degrees must be similar because triangles that are similar share the same angles.Is this proper?
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### The position of a ladder leaning against a wall and touching a box under it

I was reading a newspaper and there was a little math riddle, I thought "how funny, that's gonna be easy, let's do it" and here am I... The problem goes as follow : in a barn, there is a 1 meter ...
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### Find angles between sides of triangle and coordinate planes ($xy,yz,zx$ planes) using three 3d vectors .

Given the following, three vectors: \begin{align*} \vec{a}& = 3i−2j+5k, \\ \vec{b}& =i−6j+6k, \\ \vec{c}& =2i+3j−k, \\ \end{align*} find the angles between sides of triangle and ...
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### Is it possible to find the vertices of an equilateral triangle given its center point?

I was wondering how to find the vertices of an equilateral triangle given its center point? Such as: ...
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### Find perimeter and angle of triangle using three 3d vectors .

Given the following, three vectors: $$\vec{a} = 3\mathrm{i} - 2\mathrm{j} + 5\mathrm{k}\\\vec{b} = \mathrm{i} - 6\mathrm{j} + 6\mathrm{k}\\\vec{c} = 2\mathrm{i} + 3\mathrm{j} - \mathrm{k},\\$$ find ...
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### Minimum value of cosA+cosB+cosC in a triangle ABC

I have used jensen's inequality but couldn't move on.
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### How would you find the length of a side of a triangle where 2 sides are known and the length of a line in the middle is also known?

How would you find the length of a side of a triangle where the other 2 side lengths are known and the length of a another line that meets at the same point is known? I know there has to be an answer ...
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### Proving that $ABC$ is similar to $DQP$

Let $G$ be the centroid of triangle $ABC$. Let $D$ be the midpoint of $BC$. A line through $G$ parallel to $BC$ meet $AB$ at $M$ and $AC$ at $N$. $MC$ meets $BG$ at $P$ and $NB$ meets $CG$ at $Q$. ...
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### Alternative proof for the equality of two angles in an isosceles triangle.

From the answers of my previous question, I got an idea to prove equality of two angles in an isosceles triangle. In that question the equality of two angles in a right-angled-isosceles triangle was ...
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### Generalization to higher dimensions of a statement about plane triangles

Let $\Delta=\Delta ABC$ be a plane triangle with area $F_\Delta$ and let $P$ be a point in $\Delta$. Draw lines through $P$ parallel to the sides of $\Delta$; then $\Delta$ is decomposed into three ...
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### How is $\sin 45^\circ=\frac{1}{\sqrt 2}$?

I've been reading about the proof of $\sin 45^\circ=\dfrac{1}{\sqrt 2}$ in my book. They did it as following, let $\triangle ABC$ be an isosceles triangle as shown, Since the triangle is isosceles ...
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### Elementary problem in geometry [closed]

The problem asks to find the angle at $C$. The distance between $A$ and $B$ is $12 \space m$ and the distance between $B$ and $C$ is $8\space m$. Anyone got an idea?
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### Question related to triangles.

I am stuck at a question: O is a point in the interior of ∆PQR , then which of the following is true: 1)$(OP+OQ+OR)<1/2(PQ+QR+PR)$ 2)$(OP+OQ+OR)=1/2(PQ+QR+PR)$ 3)$(OP+OQ+OR)>1/2(PQ+QR+PR)$ ...
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### Special triangles

I have this question that I have the answer to but no working how to get it, is it by pure memorization of angles or there some steps? Without a calculator, determine, in radians, the angles of a ...
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