30-60-90 Triangle Problems

The video tutorial explains how to solve 30-60-90 triangles, highlighting the consistent side ratios of 1, 2, and √3. It provides examples of solving these triangles when given different known sides, such as the side opposite 30 degrees, the side opposite 60 degrees, and the hypotenuse. The key to solving these problems is setting up an equation to find the variable X, which represents the multiplier for the side ratios, and then using it to determine the lengths of the remaining sides.

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

• 1:2:√2

• 1:2:√3

• 1:1:√2

• 1:√3:2

If the side opposite the 30-degree angle is 5 feet, what is the length of the hypotenuse?

• 15 feet

• 5√3 feet

• 10 feet

• 5 feet

Given a 30-60-90 triangle with the side opposite the 30-degree angle as 5 feet, what is the length of the side opposite the 60-degree angle?

• 15 feet

• 5√3 feet

• 10 feet

• 5 feet

If the side opposite the 60-degree angle is 9 cm, what is the value of X?

• 3 cm

• 3√3 cm

• 9 cm

• 9√3 cm

For a 30-60-90 triangle with the side opposite the 60-degree angle as 9 cm, what is the length of the hypotenuse?

• 3 cm

• 3√3 cm

• 9 cm

• 6√3 cm

If the hypotenuse of a 30-60-90 triangle is 4 meters, what is the value of X?

• 1 meter

• 3 meters

• 4 meters

• 2 meters

Given a 30-60-90 triangle with a hypotenuse of 4 meters, what is the length of the side opposite the 30-degree angle?

• 1 meter

• 3 meters

• 4 meters

• 2 meters

For a 30-60-90 triangle with a hypotenuse of 4 meters, what is the length of the side opposite the 60-degree angle?

• 4 meters

• 2 meters

• 4√3 meters

• 2√3 meters

What is the first step in solving a 30-60-90 triangle problem?

• Set up an equation to solve for X

• Divide all sides by √3

• Multiply all sides by 2

• Find the hypotenuse

Once you have the value of X in a 30-60-90 triangle, what can you determine?

• The area of the triangle

• The perimeter of the triangle

• The angles of the triangle

• The lengths of the remaining sides