Chapter 7.4 Special Right Triangles

Front

What are the special right triangles commonly studied in geometry?

Back

The special right triangles commonly studied are the 45-45-90 triangle and the 30-60-90 triangle.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of each leg.

Front

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

Back

In a 30-60-90 triangle, the length of the side opposite the 30-degree angle is half the length of the hypotenuse, and the length of the side opposite the 60-degree angle is √3 times the length of the shorter leg.

Front

How do you find the height of an equilateral triangle with side length 's'?

Back

The height 'h' of an equilateral triangle can be found using the formula h = (√3/2) * s.

Front

What is the formula for the area of a triangle?

Back

The area 'A' of a triangle can be calculated using the formula A = (1/2) * base * height.

Front

How do you simplify radical expressions?

Back

To simplify radical expressions, factor out perfect squares from under the radical and simplify accordingly.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

Front

What is the approximate value of √3?

Back

The approximate value of √3 is about 1.732.

Front

How do you convert between degrees and radians?

Back

To convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π.

Front

What is the significance of the 30-60-90 triangle in real-world applications?

Back

The 30-60-90 triangle is often used in construction and design, as it helps in determining heights and distances in various applications.