SohCahToa, Special Right Triangles, Incenter and Circumcenter

Front

What does SohCahToa stand for in trigonometry?

Back

SohCahToa is a mnemonic for the definitions of the sine, cosine, and tangent functions: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.

Front

What are the special right triangles and their angle measures?

Back

The special right triangles are the 45-45-90 triangle and the 30-60-90 triangle. In a 45-45-90 triangle, the angles are 45°, 45°, and 90°, and the sides are in the ratio 1:1:√2. In a 30-60-90 triangle, the angles are 30°, 60°, and 90°, and the sides are in the ratio 1:√3:2.

Front

What is the definition of the incenter of a triangle?

Back

The incenter of a triangle is the point where the angle bisectors of the triangle intersect. It is also the center of the circle inscribed within the triangle.

Front

How do you find the length of the hypotenuse in a right triangle?

Back

To find the length of the hypotenuse in a right triangle, you can use the Pythagorean theorem: a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

Front

What is the circumcenter of a triangle?

Back

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. It is the center of the circle that passes through all three vertices of the triangle.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2, where the side opposite the 30° angle is 1, the side opposite the 60° angle is √3, and the hypotenuse is 2.

Front

What is the formula for the area of a triangle using the inradius?

Back

The area of a triangle can be calculated using the formula: Area = r * s, where r is the inradius and s is the semi-perimeter of the triangle.

Front

How do you calculate the inradius of a triangle?

Back

The inradius (r) of a triangle can be calculated using the formula: r = Area / s, where Area is the area of the triangle and s is the semi-perimeter.

Front

What is the significance of the angle bisector in a triangle?

Back

The angle bisector of a triangle divides the angle into two equal parts and intersects the opposite side at a point that is proportional to the lengths of the other two sides.

Front

What is the relationship between the circumcenter and the vertices of a triangle?

Back

The circumcenter is equidistant from all three vertices of the triangle, meaning the radius of the circumcircle is the same for each vertex.