How do we determine the relationships of a 45 45 90 triangle

The video tutorial explains the properties and relationships of 45-45-90 degree triangles, a type of isosceles right triangle. It begins by introducing the concept of right triangles and the importance of the Pythagorean theorem. The tutorial then delves into the specific properties of isosceles right triangles, including equal side lengths and angles. It demonstrates how to apply the Pythagorean theorem to calculate missing side lengths, particularly focusing on deriving the formula for the hypotenuse in 45-45-90 triangles, which is the leg length multiplied by the square root of 2.

What is a key characteristic of a 45-45-90 triangle?

• It is an equilateral triangle.

• It has one angle of 90 degrees and two angles of 30 degrees.

• It has two equal sides and a right angle.

• It has two equal angles of 60 degrees.

Which theorem is used to find the missing lengths in a right triangle?

• Sine Rule

• Tangent Rule

• Cosine Rule

• Pythagorean Theorem

How are the angles in a 45-45-90 triangle determined?

• By using the sine rule.

• By dividing the right angle equally between the two other angles.

• By subtracting 90 degrees from 180 and dividing the remainder equally.

• By assuming one angle is 60 degrees.

What is the relationship between the legs in a 45-45-90 triangle?

• One leg is twice the length of the other.

• The legs are in a 3:4 ratio.

• One leg is half the length of the hypotenuse.

• Both legs are equal in length.

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

• a * 2

• a * sqrt(2)

• a / sqrt(2)

• a * sqrt(3)