In this lesson, we will introduce you to the different types of angles and triangles in trigonometry.

Types of Angles: There are different types of angles in trigonometry, including acute angles, obtuse angles, right angles, straight angles, and reflex angles.

- Acute angles: An acute angle is an angle that measures less than 90 degrees.
- Obtuse angles: An obtuse angle is an angle that measures between 90 and 180 degrees.
- Right angles: A right angle is an angle that measures exactly 90 degrees.
- Straight angles: A straight angle is an angle that measures exactly 180 degrees.
- Reflex angles: A reflex angle is an angle that measures between 180 and 360 degrees.

Types of Triangles: There are different types of triangles in trigonometry, including scalene triangles, isosceles triangles, equilateral triangles, acute triangles, obtuse triangles, and right triangles.

- Scalene triangles: A scalene triangle is a triangle with three unequal sides and three unequal angles.
- Isosceles triangles: An isosceles triangle is a triangle with two equal sides and two equal angles.
- Equilateral triangles: An equilateral triangle is a triangle with three equal sides and three equal angles.
- Acute triangles: An acute triangle is a triangle with three acute angles, or angles that measure less than 90 degrees.
- Obtuse triangles: An obtuse triangle is a triangle with one obtuse angle, or an angle that measures between 90 and 180 degrees.
- Right triangles: A right triangle is a triangle with one right angle, or an angle that measures exactly 90 degrees.

Applications: Different types of angles and triangles are used in various fields such as engineering, physics, and architecture. For example, acute angles and obtuse angles are used to measure the angles of buildings and bridges, while equilateral triangles are used in construction to ensure the stability and balance of structures.

Conclusion: In conclusion, understanding the different types of angles and triangles is essential in trigonometry. There are five types of angles, including acute angles, obtuse angles, right angles, straight angles, and reflex angles. There are six types of triangles, including scalene triangles, isosceles triangles, equilateral triangles, acute triangles, obtuse triangles, and right triangles. The knowledge of different types of angles and triangles is crucial for solving problems in various fields such as engineering, physics, and architecture.