9.2 special right triangles

Front

What are the side ratios of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the side lengths are in the ratio 1 : √3 : 2. The shortest side (opposite the 30° angle) is x, the longer leg (opposite the 60° angle) is x√3, and the hypotenuse is 2x.

Front

What are the side ratios of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the side lengths are in the ratio 1 : 1 : √2. Both legs are of equal length, and the hypotenuse is √2 times the length of one leg.

Front

How do you find the length of the hypotenuse in a 45-45-90 triangle?

Back

To find the length of the hypotenuse in a 45-45-90 triangle, multiply the length of one leg by √2.

Front

What is the formula for the diagonal of a square in terms of its side length?

Back

The length of the diagonal (d) of a square with side length (s) is given by the formula d = s√2.

Front

How do you find the height of an equilateral triangle using the 30-60-90 triangle theorem?

Back

To find the height (h) of an equilateral triangle with side length (s), use the formula h = (s√3)/2.

Front

What is the relationship between the angles and sides in a special right triangle?

Back

In special right triangles, the angles determine the ratios of the sides. For example, in a 30-60-90 triangle, the angles dictate the specific ratios of the sides.

Front

What is the approximate height of a 30-60-90 triangle with a short leg of length 16?

Back

The height (long leg) of a 30-60-90 triangle with a short leg of length 16 is 16√3.

Front

How do you derive the height of a triangle from its side lengths?

Back

To derive the height of a triangle from its side lengths, you can use the Pythagorean theorem or the properties of special right triangles.

Front

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

Back

The 30-60-90 triangle is significant in real-world applications such as architecture, engineering, and design, where specific angle and side length relationships are crucial.

Front

How can you use the Pythagorean theorem with special right triangles?

Back

You can use the Pythagorean theorem to verify the relationships between the sides of special right triangles, ensuring that a² + b² = c² holds true.