5
votes
3answers
235 views

Need algebra tip about $a^4 + b^4 + c^4 - 2b^2c^2 - 2a^2b^2 - 2a^2c^2$ for sides of a triangle

I just got a long expression: $$a^4 + b^4 + c^4 - 2b^2c^2 - 2a^2b^2 - 2a^2c^2$$ and I need to prove its less than zero for every $a$, $b$, and $c$ which are triangle sides I really need tips how to ...
1
vote
3answers
37 views

Is this triangle question missing information?

In the $\Delta KLP$, find $a+b$: My question is that: isn't some information missing from the question? Because all I can see is is that $ \usepackage{ gensymb } \angle SKP = \angle LTS = ...
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 ...
0
votes
1answer
15 views

How to find last pt of triangle

How to find last pt of triangle. I got (1,7) and (0.5, 4). The equations are y = 3|2x − 1| + 4 and y = −|x − 4| + 10
1
vote
1answer
113 views

How do I solve for the height of a triangle?

The basic triangle looks something like this: How do I solve for $h$? As an example, in one problem I was given $b = 45, c = 42, \angle C = 38^\circ$ I understand how $h$ divides $\triangle ABC$ ...
0
votes
2answers
86 views

Solving all possible triangles?

So we're doing oblique triangles -- Law of Sines and all that good stuff =). I have a bunch of problems that ask you to solve for "all possible triangles that satisfy the given conditions". For ...
0
votes
2answers
48 views

Question on inscribed equilateral triangle

Question: $ABC$ and $ODE$ are equilateral triangle with $BC || DE$. If $O$ is the center of the circle, then find the ratio $AQ:QC$ So, my thought on this is that, since we are not given the ...
1
vote
0answers
77 views

Question on Proof of Shoelace Formula

I was looking for a way to prove the shoelace formula when I found this proof: For this clockwise order to make sense, you need a point O inside the polygon so that the angles form $OA_{i}A_{i+1}$ ...
0
votes
1answer
107 views

Correct my Pre-Calculus work please?

PPlease explain how to do these problems. I got my test back and I'm trying to see what I did wrong so I can do better on the next test. Given $g(x)=\sqrt{x+5}$ find $g^{-1}$ $x= \sqrt{y+5}$, I ...
3
votes
2answers
80 views

Generating Pythagorean Triples S.T. $b = a+1$

I am looking for a method to generate Pythagorean Triples $(a,b,c)$. There are many methods listed on Wikipedia but I have a unique constraint that I can't seem to integrate into any of the listed ...
-1
votes
1answer
34 views

Trianlgle homework [closed]

The triangle formed by $$A(-2,-3) ,~~ B(1,3),~~ C(10,k)$$ is right-angled triangle at $A$, find: a) the value of $k$, b) the area of triangle $ABC$, c) The length of $AM$ where $M$ is the mid-point ...
8
votes
4answers
188 views

equilateral triangle; $3(a^4 + b^4 + c^4 + d^4) = (a^2 + b^2 + c^2 + d^2)^2.$

In equilateral triangle ABC of side length d, if P is an internal point with PA = a, PB = b, and PC = c, the following pleasingly symmetrical relationship holds: $3(a^4 + b^4 + c^4 + d^4) = (a^2 + b^2 ...
1
vote
4answers
154 views

Where does $\sin 3° =3\sin 1° -4 \sin^3 1°$ come from?

Wikipedia makes the claim: "Though a complex task, the analytical expression of $\sin 1°$ can be obtained by analytically solving the cubic equation $\sin 3° =3\sin 1° -4 \sin^3 1°$ from whose ...
4
votes
2answers
219 views

$x \sin x=2$ why is my proof that there no solutions wrong?

$\frac 12 x \sin x=1$ . Let's look at a right triangle with base $x$ and altitude $\sin x$ . Then our equation is for the area of this triangle. Let the sides of the triangle be $a=x$ , $b=\sqrt ...
0
votes
2answers
924 views

Minimizing (and maximizing) the area of triangles

How would one solve questions like this one here in general? I have gotten an answer for that question, but I don't understand what's the intuition behind it. Can smoeone clearly explain how to ...
0
votes
2answers
110 views

Angular radius of a sphere

Given a sphere with radius $r$ about a point $c$, what's the apparent angular radius $\alpha$ of that sphere from point $P$? In other words, if $\vec{o} = c - P$, what's the maximum angle another ...
0
votes
2answers
1k views

Deriving the formula for the radius of the circle inscribed in an equilateral triangle

I am trying to derive the formula for the radius of the circle inscribed in an equilateral triangle from scratch. Given $2*n$ = length of a side $H$ = the altitude of the triangle = $h + a$ ...
16
votes
1answer
62k views

Solving Triangles (finding missing sides/angles given 3 sides/angles)

What is a general procedure for "solving" a triangle—that is, for finding the unknown side lengths and angle measures given three side lengths and/or angle measures?
0
votes
4answers
4k views

Solving a triangle given two side lengths and the measure of a non-included angle

Let's say given an angle A = 46 °, side a = 2.29 and b = 2.71 I figured that the angle B = 58.4 by saying: $$B = \sin^{-1} \left(\frac{ 2.71 \sin{46^{\circ}}}{2.29}\right)=58.4^{\circ}$$ But I ...
0
votes
2answers
2k views

Solving a triangle, given two sides and the measure of the included angle

Let say you have a triangle Angle A = 41 degrees , side b = 3.41 and c = 5.83 can you use pythagoras theorem to find the side a? and how can you find Angle B and C
2
votes
1answer
366 views

Find angles using the Law of Cosines

if you must find the Angle C based on the sides of a = 2, 3 b = 4,6 og c = 5, 9  I have used the formula: $$\cos (C) =\frac{a^2 + b^2-c^2}{2ab}$$ use, but I think i'm doing something wrong: ...
0
votes
1answer
1k views

Solving triangles and quadratic equations

When calculating the pieces in a triangle with only two sides and an intermediate angle is known, one must solve a quadratic equation. By solving the equation are 2, 1 or 0 solutions, as ...
1
vote
3answers
303 views

Systems of equations finding right triangles

I need help setting up the equation for the question, "Find all right triangles for which the perimeter is $24$ units and the area is $24$ square units." I know that the area is $A = \frac12 b h$ ...
0
votes
1answer
79 views

Quadratic Equation related question.

So here's the question : The hypotenuse of a right triangle is $3 \sqrt 5$ cm. If the smaller side is tripled & the larger side is doubled, the new hypotenuse will be $15$ cm. Find the length of ...
0
votes
2answers
191 views

How long is side $c$ in this right triangle if $a = b$?

A right angled triangle has side lengths labeled as so. A common geometric construction that shows three squares sitting upon the sides of a right triangle with lengths A, B, and C However unlike in ...