Properties of Special Right Triangles

This video reviews two special triangles: the 30-60-90 triangle and the isosceles triangle. It explains the properties and side length ratios of each triangle. The 30-60-90 triangle has side ratios of 1, √3, and 2, while the isosceles triangle has side ratios of 1, 1, and √2. The video emphasizes the importance of memorizing these ratios for solving mathematical problems. Examples are provided to illustrate how to apply these ratios to find unknown side lengths when given one side length and the angles.

What are the two types of special triangles discussed in the video?

• Acute and isosceles triangles

• Equilateral and scalene triangles

• Right and obtuse triangles

• 30-60-90 and 45-45-90 triangles

Which angle is opposite the side with length 1 in a 30-60-90 triangle?

• 45-degree angle

• 90-degree angle

• 60-degree angle

• 30-degree angle

What is the length of the hypotenuse in a 30-60-90 triangle if the side opposite the 30-degree angle is 1?

• Square root of 2

• 2

• Square root of 3

• 1

If the side opposite the 30-degree angle in a 30-60-90 triangle is 10, what is the length of the hypotenuse?

• 5

• 15

• 20

• 10

In a 30-60-90 triangle, if the side opposite the 60-degree angle is 5√3, what is the length of the side opposite the 30-degree angle?

• 15

• 5

• 5√3

• 10

What are the angles in an isosceles 45-45-90 triangle?

• 90, 45, 45 degrees

• 60, 60, 60 degrees

• 45, 45, 90 degrees

• 30, 60, 90 degrees

In a 45-45-90 triangle, what is the ratio of the lengths of the legs to the hypotenuse?

• 1:1:√2

• 1:√3:2

• 1:2:√3

• 1:1:2

If one leg of a 45-45-90 triangle is 4 cm, what is the length of the hypotenuse?

• 4 cm

• 4√2 cm

• 8 cm

• 2√2 cm

In a 45-45-90 triangle, if the hypotenuse is 8 cm, what is the length of each leg?

• 4√2 cm

• 8√2 cm

• 8 cm

• 4 cm

What is the length of the hypotenuse in a 45-45-90 triangle if each leg is 7 cm?

• 7 cm

• 14√2 cm

• 14 cm

• 7√2 cm