Special Right Triangles and Ratios

This video tutorial covers solving special right triangles, focusing on 30-60-90 and 45-45-90 triangles. It explains the side ratios for these triangles and demonstrates how to use these ratios to solve for unknown sides. The video provides examples for both types of triangles, emphasizing the importance of understanding these ratios for solving problems efficiently.

What is the ratio of the sides in a 30-60-90 triangle?

• 1:1:√2

• 1:√3:2

• 2:1:√3

• 1:2:√3

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

• 10

• 10√3

• 5√3

• 5

In a 30-60-90 triangle, if the side opposite the 60-degree angle is 6, what is the hypotenuse?

• 4√3

• 6

• 12

• 6√3

In a 30-60-90 triangle, if the side opposite the 30-degree angle is 4, what is the hypotenuse?

• 4√3

• 8

• 4

• 8√3

What is the ratio of the sides in a 45-45-90 triangle?

• 1:√3:2

• 1:2:√3

• 1:1:√2

• 2:1:√3

If one leg of a 45-45-90 triangle is 7, what is the length of the hypotenuse?

• 14

• 14√2

• 7

• 7√2

In a 45-45-90 triangle, if the hypotenuse is 10, what is the length of each leg?

• 10

• 5√2

• 5

• 10√2

If the side opposite the 45-degree angle in a 45-45-90 triangle is 8, what is the hypotenuse?

• 16√2

• 8

• 16

• 8√2

If the hypotenuse of a 45-45-90 triangle is 12, what is the length of each leg?

• 12

• 12√2

• 6√2

• 6

What is the significance of knowing the side ratios in special right triangles?

• It simplifies solving these specific triangles.

• It is not significant.

• It is only useful for equilateral triangles.

• It helps in solving any triangle.