1
vote
2answers
56 views

Trigonometry and triangle proof

Question: Prove that in an acute angle triangle ABC: $$\tan A\tan B +\tan A \tan C + \tan B \tan C \geq 9$$ I have no idea where to even begin this question. Please help me!
0
votes
2answers
68 views

In any triangle ABC, the expression (a + b + c) (a + b - c) (b + c - a) (c + a - b)$ is equal to

In any triangle ABC, give an equivalence to the expression $$(a + b + c) (a + b - c) (b + c - a) (c + a - b)$$ Can somebody help me? Note that ...
0
votes
2answers
49 views

Find the value of $a$.

please help I'm lost on what numbers to add or what formula to use
0
votes
1answer
21 views

Translate line vertically and calculate intersection on circle

Let's say I have a line extending from the center of the circle at a 45° angle. If I were to translate that line up 212.132 units, how would I calculate the intersection between the translated ...
1
vote
1answer
23 views

$S$, $I$, $O$ are circumcenter, incenter and orthocenter then $SO\ge IO \sqrt2$

Let $S$, $I$ and $O$ be the circumcenter, incenter and orthocenter of $\triangle ABC$ then prove that $SO\ge IO \sqrt2$, or equivalently $SO^2\ge 2IO^2$. I was able to derive an expression for $SO^2$ ...
1
vote
0answers
13 views

Complete Triangle Given 3 Parallel Planes and 2 Points

I have a problem where a point B connects to a point C at a known angle and distance. Both point B and C are on two separate parallel axis, GH and JK respectively. I need to find a third point, A, on ...
0
votes
0answers
33 views

Translate vertical movement into radial movement?

I've tried all sorts of things, but I'm no mathematician and I've conceded defeat. So I come here for help. I don't know if I really worded the question correctly since I don't even know what I should ...
0
votes
1answer
45 views

Triangle question, proving isoceles given trigometric conditions

$ABC$ is a triangle satisfying the following condition: $$\frac{\sin B}{\sin A}=\frac{\tan B+\cot C}{\tan A+\cot C}$$ How do I prove that $ABC$ is isoceles? I really have no idea.
0
votes
2answers
30 views

How do I find a missing angle using a reciprocal trigonometric function?

I just attempted this as best as I could, but I'm not sure if I'm correct. Here's the work: $$\cot x =\frac{1}{2}$$ $$\frac{1}{\tan{x}} = \frac{1}{\frac{1}{2}}$$ $$\frac{1}{\tan^{-1}\cdot\tan x} = ...
1
vote
1answer
32 views

Splitting a triangle to make two equal halves, find the length of the new line

Could someone please explain to me how I would find this out? I have a triangle and I need to find the length of the line that would split it down the middle so that the areas were even. A = 105 ...
1
vote
2answers
52 views

Find the angle between the sides 4 and 7 in a right triangle

I need to solve the $B$ corner What I've tried: $$\operatorname{sin} B=\frac47$$ $$B=\operatorname{arcsin}\frac47$$ $$B=34.85$$ But that's not the right answer, can anyone help me find what I did ...
0
votes
4answers
46 views

How to find an angle (in degrees) in a right triangle, given its sides?

I need to find out a degree of an angle. Pretty simple, or so I thought. I remember doing a crap-ton of these in high-school, sadly the details did not remain. Anyway, let's take a look at this ...
1
vote
3answers
31 views

Basic question about angles

Why is the answer a)? Why can't it be d)? Why are the choices listed in this format, i.e., $(x \pm \theta^{\circ})$, and why is angle C $(x+30^{\circ})$ and not just $30^{\circ}$? Thanks.
-1
votes
1answer
66 views

How to get the third point coordinates in isosceles triangle?

Isosceles triangle $ABC$ $AB = AC = d_1$ $BC = d_2$ $A = (x_1, y_1)$ $B = (x_2, y_2)$ $C = (x_3, y_3)$ $\angle BAC = \phi$ $\angle ABC =\angle ACB = \theta$ I want an equation for $x_3$ and $y_3$ ...
2
votes
1answer
65 views

Trigonometric Substitution and the Triangle Inequality

I was reading the solution to this problem: If $x, y, z$ are real numbers and $x+y+z=xyz$ then $x(1 − y^2 )(1 − z^2 ) + y(1 − z^2 )(1 − x^2 ) + z(1 − x^2 )(1 − y^2 ) = 4xyz$ The solution is to ...
0
votes
1answer
23 views

Find points of triangle, one point, all sides and all angles known

Imagine the setup above; how can I calculate the points P1 and P2 if all angles, all sides A,B,C and point P3 are known?
0
votes
0answers
33 views

Trigonometry, find distance of arc movement

Imagine I have the setup as follows: I want to compute the height x in State 2, depending on how much the blue axis have moved. That is, the distance ...
0
votes
0answers
31 views

Similar triangle, Quick question (Thick Lens Formula)

http://www.panohelp.com/thinlensformula.html On the right hand side, f is defined as focus of the lens, i understand why the image distance is (f + fm). However i have spent an afternoon and could ...
2
votes
1answer
38 views

Ratio of sides of Triangle $ABC$

if in a Triangle $\Delta ABC$ with $a$, $b$ and $c$ as sides $$\begin{align}\left(Cot\frac{A}{2}\right)^2 ...
2
votes
3answers
75 views

Finding an area of a triangle inside of a triangle, given certain areas of other triangles, and area ratios.

I'm studying for the Waterloo Math Contest (Galois, Gr. 10) taking place in April of 2015 and I am preparing by looking at previous problems and solving them. This is question 4(c) on the 2010 Galois ...
1
vote
2answers
40 views

How to find length of the sides of a triangle given the ratio of the sines of the sides?

Consider $\triangle ABC$. Let $\dfrac{\sin A}{\sin B} = \dfrac56$ and $\dfrac{\sin B}{\sin C} = \dfrac45$. Find $\dfrac{\vert AC\vert\cdot \vert AB\vert}{\vert BC\vert}$. If there is no definite ...
1
vote
2answers
458 views

Solving for Cos Exactly

How to solve $\cos(\dfrac{5\pi}{6})$ and $\cos(\dfrac{7\pi}{6})$ exactly? I couldn't use special triangles to solve this either.
2
votes
2answers
34 views

Get the angle in a circle using center, radius and one point in a circle.

There is a circle and i know Point1 this is fixed and i know another point Point2 which can be anywhere in the circle. and i want to know the angle which is made at center. Thanks Your help will be ...
0
votes
4answers
96 views

Finding $\sin^{-1}(x)$ without using a calculator

I don't understand how to compute $\sin^{-1} (0.6293)$, to figure out the angle without using a calculator. I understand how to find the answer if I use a calculator but I don't understand the ...
1
vote
2answers
27 views

Find length of $CD$ where $\angle BCA=120^\circ$ and $CD$ is the bisector of $\angle BCA$ meeting $AB$ at $D$

$ABC$ is a triangle with $BC=a,CA=b$ and $\angle BCA=120^\circ$. $CD$ is the bisector of $\angle BCA$ meeting $AB$ at $D$. Then the length of $CD$ is ____ ? A)$\frac{a+b}{4}$ B)$\frac{ab}{a+b}$ ...
0
votes
0answers
15 views

Rotating a triangle in different coordinate systems.

My android application uses openGL. OpenGL coordinate system has the origin in the middle and goes from -1 to 1. When I am rotating an equilateral triangle in the openGL coordinates, the triangle ...
0
votes
0answers
55 views

Calculate height from two right angled triangles sharing an edge

I am trying to calculate the perpendicular distance of a unicycle-like robot from a wall using two successive measurements from an ultrasonic sensor. The problem is modelled as shown: (EDIT). The ...
1
vote
0answers
45 views

Rationality in Triangle

How can I justify this answer? I think the answer is infinite, but cannot justify it///
1
vote
1answer
40 views

Is the given triangle unique?

I was reading Polya's How to Solve It when I came across the following problem. Construct a triangle with an angle, the length of altitude through that angle and the perimeter of the triangle given. I ...
0
votes
3answers
106 views

find angle sine knowing all sides

I know all the sides of an arbitrary triangle but not the angles, and I want to find the sine of any angle. ...
0
votes
1answer
49 views

To prove inequality for two similar triangles $ABC$ and $A_1B_1C_1$ given that $A_1B_1C_1$ is inscribed in $ABC$

Consider a triangle $ABC$. A directly similar triangle $A_1B_1C_1$ is inscribed in the triangle $ABC$ such that $A_1,\;B_1\;,C_1$ are the interior points of the sides $AC,\;AB\;and\;BC$ respectively. ...
1
vote
1answer
29 views

Find Coordinates on a track

Charlie and Alexandra are running around a circular track with radius 60 meters. Charlie started at the westernmost point of the track, and, at the same time, Alexandra started at the northernmost ...
0
votes
2answers
41 views

Finding coordinates on a circle

So this problem I am have difficulty with. I think where I am going wrong is how to calculate the initial theta. Do I just use pi/2 because in the pictures it show to angle theta off the 90 degree ...
0
votes
1answer
36 views

Find the height of the dam given angles of a triangle

The top of a dam has an angle of elevation of 1.3 radians from a point on a river. Measuring the angle of elevation to the top of the dam from a point 155 feet farther downriver is 0.8 radians; assume ...
1
vote
1answer
89 views

Finding the missing coordinate of a point within a 3D triangle

We have an equilateral triangle $ABC$ in 3-dimensional space. The points are known, such as: $A = (x_1,y_1,z_1)$ $B = (x_2,y_2,z_2)$ $C = (x_3,y_3,z_3)$ Point $P$ is on triangle $ABC$. If I know ...
0
votes
1answer
20 views

calculate the angles of a triangle?

If we have a triangle $ABC$ and we only know three things: -The angle $A$ -The length $AB$ -The length $AC$ Is it possible to calculate the other angles: $B$, $C$ All what I can think of ...
3
votes
1answer
84 views

Proving a tough geometrical inequality, with equality in equilateral triangles.

For any triangle with sides $a ,b, c$ prove or disprove (1) and (2) : $$\sum_\mathrm{cyc} \frac{1}{\frac{(a+b)^2-c^2}{a^2}+1}\ge \frac34$$ Equality in (1) holds if and only if the triangle is ...
0
votes
1answer
42 views

Year 10 - Trigonometry

Please ignore the pencilled 4m in the diagram but I really need to know what the length of the bottom line - line DC - is. A procedure or tips on how to calculate this would be useful. Also, is the ...
5
votes
1answer
126 views

If this relation holds, then is the triangle equilateral?

Let $ABC$ be a triangle. If $$\sum_{cyc}\frac{BC}{4AC\cos^2({\frac{\angle BAC}{2})}+BC}=\frac{3}{4}$$ then the triangle is equilateral? We can check if we set $\widehat{BAC}=\pi/3$ and $AB=BC=CA$ that ...
0
votes
1answer
18 views

New Angle When Opposite Side is Halved

Suppose you have a right triangle with any length sides. The value of one of the angles is $\theta$ and the opposite side is a. If I change the triangle so that the new length of side a is $\frac a2$, ...
3
votes
1answer
108 views

Inequality problem about sides of a triangle and the semiperimeter

Let $a,b,c$ the sides of a triangle and $s$ be the semi perimeter. Then show that $$ a^2+b^2+c^2 > \frac{36}{35}(a^2+\frac{abc}{s}) $$ I tried it doing in many ways using some ...
0
votes
1answer
35 views

An Inverse Cosine Problem

Here is my problem: $$ \sin(\cos^{-1} \frac{2}{5} ) $$ I know how to do it for the most part; I just draw a triangle with sides 2,5 and √21 and I then find the sine (opposite/hypotenuse) of the ...
1
vote
1answer
33 views

Sin and Cos relationship with Triangle sides

In a triangle ABC, ${sinA < \frac{a}{c}}$ and ${cosA > \frac{b}{c}}$. Which of the statements below are always false regarding triangle ABC? ABC is an acute triangle ABC is an isosceles ...
0
votes
1answer
20 views

Using Right triangles to determine Values

Missed a day of class, and I can't seem to figure out the concept here. It seems simple but I just can't wrap my head around it. Any and all help is much appreciated.
0
votes
1answer
33 views

Question that includes Trigonometry

In the diagram, $AB = 80 cm$, $\angle ABD = 44^∘$ (Angle B), $\angle BAC = 31^∘$, $\angle DAC =37^∘$ and $\angle DBC = 36^∘$. Calculate: a) $BC$ b) $BD$ c) $CD$
0
votes
1answer
16 views

Find term for one angle of two in a trig function

In a right angled triangle, I know that $\tan (x) = \cfrac{4}{z}$ and that $\tan(x+y) = \cfrac{12}{z}$. I need to find an equation which has only $\tan(y)$. The answer is $\cfrac{12}{z} = ...
0
votes
1answer
24 views

Finding angles in Barycentric system

How to find the angles of a triangle given the barycentric coordinates of its corners? Does it work if i take the first two components of every coordinate, and find the angles in the triangle (on the ...
0
votes
1answer
42 views

Solve an Angle-Side-Angle special case triangle if it has an obtuse angle?

I've seen this type of problem multiple times on homework, and it's confusing me like mad. The scenario: We have a triangle. It is a special case triangle, with one angle, one side, and another ...
2
votes
2answers
277 views

How to find opposite and adjacent lengths of a right triangle given the hypotenuse and angle?

I'm writing a few functions for a JavaScript game engine. Is it possible to calculate the length of the legs of a right triangle given ONLY the length of the hypotenuse and an angle?
0
votes
1answer
15 views

Obtaining consistent triangle surface normals.

I am given 3 points in a random order like so... calculateSurfaceNormal(point1, point2, point3); I have implemented the method by simply saying... ...