Tree angles have the sizes 94°, 36.5°, and 49.5. Is it possible that these angles are in a triangle?
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Tree angles have the sizes 94°, 36.5°, and 49.5. Is it possible that these angles are in a triangle?
Let's remember that the sum of angles in a triangle is equal to 180 degrees.
We'll add the three angles to see if their sum equals 180:
Therefore, these could be the values of angles in some triangle.
Possible.
The triangle ABC is shown below.
To which side(s) are the median and the altitude drawn?
In mathematics, close isn't good enough - the sum must be exactly 180°. If you get 179.8° or 180.3°, those angles cannot form a triangle.
Absolutely! Angles can be any positive decimal value. What matters is that they're all less than 180° individually and sum to exactly 180° together.
No! The order doesn't matter for checking if angles can form a triangle. Whether you have 94°, 36.5°, 49.5° or 49.5°, 94°, 36.5°, the sum is still the same.
That's fine! Triangles can have obtuse angles (greater than 90°) as long as the total still equals 180°. In this problem, 94° makes it an obtuse triangle.
Line up the decimal points and add column by column:
94.0 + 36.5 + 49.5
Start with whole numbers (94 + 36 + 49 = 179), then decimals (0.0 + 0.5 + 0.5 = 1.0), giving 180.0°
Yes! Each individual angle must be greater than 0° and less than 180°. But the most important rule is that all three must sum to exactly 180°.
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