30-60-90 Triangle and Circle Concepts

This video tutorial covers the properties and calculations related to the 30-60-90 right triangle. It explains the side ratios and how to find missing sides using multiplication and division. Several examples are provided to illustrate these concepts, including a typical SAT math question involving a circle and a triangle. The video emphasizes understanding the relationships between the angles and sides to solve problems efficiently.

What is the length of the side opposite the 30-degree angle in a 30-60-90 triangle if the hypotenuse is 10?

• 5

• 10

• 2

• 5√3

Tags

CCSS.HSG.SRT.C.8

If you know the side opposite the 30-degree angle is 6, what is the length of the hypotenuse?

• 12

• 3

• 6

• 6√3

Tags

CCSS.HSG.CO.C.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?

• 5√3

• 10

• 15

• 5

Tags

CCSS.HSG.SRT.C.8

Given a side of 12√3 opposite the 60-degree angle, what is the length of the hypotenuse?

• 36

• 12

• 24

• 24√3

Tags

CCSS.HSG.SRT.C.8

If the hypotenuse is 16√3, what is the length of the side opposite the 30-degree angle?

• 16√3

• 16

• 8√3

• 8

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the length of the side opposite the 60-degree angle if the side opposite the 30-degree angle is 7?

• 7√3

• 7

• 14

• 21

Tags

CCSS.HSG.CO.C.10

In a 30-60-90 triangle, if the side opposite the 60-degree angle is 9, what is the length of the hypotenuse?

• 12

• 6√3

• 18

• 9√3

How do you find the area of a shaded region formed by a circle and a 30-60-90 triangle?

• Subtract the area of the triangle from the area of the circle

• Divide the area of the circle by the area of the triangle

• Add the areas of the circle and triangle

• Multiply the areas of the circle and triangle

Tags

CCSS.7.G.B.4

If the diameter of a circle is 20, what is the radius?

• 5

• 20

• 10

• 15

Tags

CCSS.7.G.B.4

What is the area of a circle with a radius of 10?

• 100π

• 50π

• 200π

• 25π

Tags

CCSS.7.G.B.4