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omicron
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Find all the angles from [tex]0^{\circ}[/tex] to [tex]360^{\circ}[/tex] inclusive which satisfy the equation
[tex]$ \tan(x-30^{\circ}) - \tan 50^{\circ} = 0 [/tex]
[tex]$ \tan(x-30^{\circ}) - \tan 50^{\circ} = 0 [/tex]
Kahsi said:[tex]\tan(\alpha + \beta) = \frac{tan(\alpha)+\tan(\beta)}{1-\tan(\alpha)\tan(\beta)}[/tex]
[tex]\tan(x - 30) = \frac{tan(x)+\tan(-30)}{1-\tan(x)\tan(-30)}[/tex]
[tex]\frac{tan(x)+\tan(-30)}{1-\tan(x)\tan(-30)}=\tan(50)[/tex]
[tex]\tan(x)+\tan(-30)=\tan(50) - \tan(x)\tan(-30)\tan(50)[/tex]
[tex]\tan(x) + \tan(x) \tan(-30)\tan(50)=\tan(50) - \tan(-30)[/tex]
[tex]\tan(x)(1 +\tan(-30)\tan(50))=\tan(50) - \tan(-30)[/tex]
[tex]\tan(x)=\frac{\tan(50) - \tan(-30)}{1 +\tan(-30)\tan(50)}[/tex]
Kahsi said:[tex]\tan(\alpha + \beta) = \frac{tan(\alpha)+\tan(\beta)}{1-\tan(\alpha)\tan(\beta)}[/tex]
[tex]\tan(x - 30) = \frac{tan(x)+\tan(-30)}{1-\tan(x)\tan(-30)}[/tex]
[tex]\frac{tan(x)+\tan(-30)}{1-\tan(x)\tan(-30)}=\tan(50)[/tex]
[tex]\tan(x)+\tan(-30)=\tan(50) - \tan(x)\tan(-30)\tan(50)[/tex]
[tex]\tan(x) + \tan(x) \tan(-30)\tan(50)=\tan(50) - \tan(-30)[/tex]
[tex]\tan(x)(1 +\tan(-30)\tan(50))=\tan(50) - \tan(-30)[/tex]
[tex]\tan(x)=\frac{\tan(50) - \tan(-30)}{1 +\tan(-30)\tan(50)}[/tex]
Yup. Thanks!Nylex said:[tex]\tan(x-30^{\circ}) = \tan 50^{\circ}[/tex]
Can you go from there?
Hence my smiliesZurtex said:It's not that complex:
Kahsi said:Hence my smilies
The "Find all the angles problem" is a mathematical problem that involves determining the measurements of all the angles in a given shape or figure. This can include various types of angles, such as acute, right, obtuse, and reflex angles.
To solve the "Find all the angles problem", you will need to use the properties and rules of angles, such as the sum of angles in a triangle or quadrilateral, and the relationships between angles formed by intersecting lines. You may also need to use tools like a protractor or ruler to accurately measure angles.
Some common strategies for solving the "Find all the angles problem" include breaking the shape into smaller, simpler shapes, using known angles and their relationships to find unknown angles, and using algebraic equations to represent the relationships between angles.
To avoid mistakes when solving the "Find all the angles problem", make sure to carefully label and organize your work, double-check your calculations, and use multiple strategies to confirm your answers. It can also be helpful to work backwards or try different methods to check your work.
The "Find all the angles problem" is relevant in various fields, such as architecture, engineering, and surveying, where accurate measurements of angles are crucial for designing and constructing buildings, roads, and other structures. It is also used in navigation and mapmaking to determine the direction and distance between two points.