All Questions
Tagged with triangles trigonometry
1,311
questions
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How do I determine angles and lengths of a triangle if I'm only given one angle and one side length. [closed]
I just don't think I can if given angles A, B, and C (where A and B are unknown and C = 90 deg) and sides a, b, and c--the sides opposite the angles--where side a is 10 in and sides b and c are ...
-2
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0
answers
50
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Olympiad geometry problem with angles [closed]
Triangle ABC has a right angle at A. Altitude AD has length 20. The bisector of angle B meets AD at K. If angle ACK= 2angle DCK, find KC. This is an olympiad practice problem which I am trying to ...
- 27
1
vote
1
answer
42
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2-D scalene obtuse triangle trigonometry.
I am struggling with this trigonometry question:
I tried using the cosine law with angle DBC
$a^2 = b^2 + c^2 - 2bc \cos A$ but you need to know the measure of the angle.
In terms of the angle Φ, the ...
0
votes
1
answer
46
views
Knowing a side, the inradius, and the circumradius of a triangle, find the other two sides [closed]
I need help with this easy triangle problem:
We know:
One of the sides a = 16 cm.
The inradius r = 6cm.
And the circumradius R = 17 cm.
That's all.
We must find the lengths of the other two sides.
...
1
vote
3
answers
219
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Parallel line equation
I want to incorporate 2 diagonal lines in a logo design. The lines have to be parallel to each other and have to be exactly 0.5 inches apart when measured perpendicular. The upper point of Line 1 has ...
- 37
0
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0
answers
36
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acute angles $\alpha$ and $\beta$ of the triangle $ABC$ satisfy $\sin^2 \alpha + \sin^2 \beta = \sin (\alpha + \beta)$, then $ABC$ is right-angled. [duplicate]
Given that the acute angles $\alpha$ and $\beta$ of the triangle $ABC$ satisfy the condition $\sin^2 \alpha + \sin^2 \beta = \sin (\alpha + \beta)$. Prove that the triangle $ABC$ is right-angled.
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user1341210
3
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6
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230
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Rotating and scaling an arbitrary triangle such that the new triangle has its vertices on the sides of the original one
Given $\triangle ABC$, and a scale factor $r \lt 1 $, I want to find the necessary rotation (center and angle) such that the rotated/scaled version of the triangle has its vertices lying on the sides ...
- 24.5k
3
votes
5
answers
94
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Minimizing $\left(\frac{c}{a} + \frac{c}{b}\right)^2$, where $c$ is the hypotenuse of a right triangle with legs $a$ and $b$
This question is regarding the following problem
Given that $a, b, c$ are the sides of the $\triangle ABC$ which is right angled at $C$, then what is the minimum value of the following expression?
$$\...
- 356
1
vote
1
answer
97
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Area of the wet part of a horizontal cylinder
So, my math teacher gave me an interesting problem on mensuration.
Given, a cylinder of Height $H$ and radius $r$ is filled with water upto height h. Then the cylinder is pushed and it lies down ...
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0
votes
1
answer
84
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alternate law of tangents?
In the response to a related question here is given a formula to compute one of the angles not given for an SAS triangle:
$$\tan(A) = \frac{\sin(C)}{\frac{b}{a}-\cos(C)}$$
where $a,b,C$ are the given ...
- 465
2
votes
2
answers
48
views
Determining a geometric angle
I have the following situation where the line $(AB)$ is orthogonal to the "vertical line" passing through $C$.
Is there a way to determine the blue angle in terms of $\boldsymbol {AC}$, $\...
- 567
1
vote
1
answer
32
views
Center of outer Soddy circle lies on the same side of lines $AC,BC$ where $AB$ is the longest side
Let $AB$ be the longest side of $\triangle ABC$.
I want to prove the center of outer Soddy circle either lies on the intersection of the inner sides of lines $AC,BC$ or lie on the intersection of the ...
- 3,047
2
votes
2
answers
142
views
Does $ \frac{\sin(\theta-\alpha)}{\sin\alpha}=\frac{\cos(\theta+\gamma-\alpha)}{\cos(\gamma-\alpha)}$ have an analytical solution for $\alpha$?
The equation is about $\alpha$:
$$ \frac{\sin(\theta-\alpha)}{\sin\alpha}=\frac{\cos(\theta+\gamma-\alpha)}{\cos(\gamma-\alpha)} \tag{1}\label{1}$$
where $\theta$ and $\gamma$ are given. I failed to ...
- 23
2
votes
2
answers
171
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How to find an acute angle of a right triangle inscribed in a square?
Working on
Daniel J. Velleman. (2017). "Calculus: A Rigorous First Course" (p. 66)
My question is focused on the purple circle on the image above. The solution given by the author is $\...
- 2,367
0
votes
1
answer
41
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Connection between trigonometric ratios and similar triangles.
Working on:
Daniel J. Velleman. (2024). "Calculus: A Rigorous First Course" (p. 63)
The author explains:
Although we have not used right triangles to define the trigonometric functions, ...
- 2,367