Villyer said:
When referring to a triangle, an obtuse angle is an angle that is greater than 90 degrees. This means that theta, or the angle in question, is larger than 90 degrees and falls within the range of 91 to 179 degrees.
This statement is often used when discussing triangles to indicate that the angle in question is not a valid angle in the given context. For example, if the discussion is about right triangles, an angle that is greater than 90 degrees (obtuse) would not make sense since right triangles have one angle that must be exactly 90 degrees.
Yes, you can determine if theta is obtuse by looking at the given information about the triangle. For example, if it is stated that the triangle is a right triangle, then theta cannot be obtuse. However, if the triangle is not specified to be a right triangle, then theta could potentially be obtuse.
No, theta cannot be both obtuse and acute at the same time. An angle can only fall into one category based on its measurement. However, theta can be either obtuse or acute depending on the given context or information about the triangle.
Knowing that theta is obtuse can affect the triangle in several ways. It can help determine the type of triangle (such as right, acute, or obtuse), the length of its sides, and the size of its other angles. It can also be used in trigonometric calculations and other mathematical applications involving triangles.