How Do You Calculate the Angle $$\gamma_{xy}'$$ in a Modified Rectangle?

In summary, the conversation is about finding an angle related to trigonometry. The person is trying to find the angle \gamma_{xy}' and is seeking advice on how to approach the problem. They mention a hint from their professor to find the sum of angle changes on both sides of the rectangle. Another person suggests using tan to find certain angles and using the rule that internal angles add up to 360 for 4-sided shapes and 180 for triangles. They also suggest assuming that certain angles are equal to each other to have more information to work with.
[SOLVED] Finding an Angle (more trig)

(#25) Okay, so I am getting a little better at this, but still not great. I have to find the angle $\gamma_{xy}'$

I have drawn the original rectangle in blue and the new elongated one in green (I exaggerated it to help clarify)

Looking at points C and C' I can see that $\gamma_{xy}'=180-\tan^{-1}\frac{300}{2}+\theta$ where theta is that little bit more. . . that is between (BC)' and the vertical. If I could find that I would be all set.

Any ideas on how to proceed? Or should I have taken a different route?

My professor's hint says 'Find the sum of the angle change of both sides AB and AD'

which I thought is more or less what I am doing?

Thanks,
Casey

Last edited:
Super awesome. Maybe it's obvious to everyone else. . .

Hi, I'm not sure which angle exactly you want to find.

You can automatically find angles DAD' and BAB' from using tan.
Then you can use the 90 degree rules to find angles in between.
Along the way you can use the internal angles summation is 360 for 4-sided shapes and 180 for triangles.

If you assume that angle C'D'C is equal to angle B'AB, and assume angle DAD' is equal to angle CB'C', you'll have more to work with.

1. How do I find an angle using trigonometric functions?

To find an angle using trigonometric functions, you need to know at least two sides of a right triangle or one side and one angle. Then, you can use the trigonometric ratios (sine, cosine, and tangent) to calculate the missing angle.

2. What is the difference between finding an angle using sine, cosine, and tangent?

The difference between using sine, cosine, and tangent to find an angle lies in the ratio used. Sine is the ratio of the opposite side to the hypotenuse, cosine is the ratio of the adjacent side to the hypotenuse, and tangent is the ratio of the opposite side to the adjacent side.

3. Can I use trigonometry to find angles in any shape?

Trigonometry can only be used to find angles in right triangles. If the shape is not a right triangle, you will need to break it down into smaller right triangles and use trigonometric functions on each one.

4. How can I use inverse trigonometric functions to find an angle?

Inverse trigonometric functions (arcsine, arccosine, and arctangent) can be used to find an angle when given the ratio of two sides. For example, if you know the ratio of the opposite side to the adjacent side, you can use the arctangent function to find the angle.

5. What are the common mistakes when finding angles using trigonometry?

Some common mistakes when finding angles using trigonometry include using the wrong trigonometric ratio, using the wrong unit of measurement (degrees vs. radians), and forgetting to use inverse trigonometric functions when necessary. It is important to carefully identify which sides and angles are given and which ones are being solved for to avoid these mistakes.

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