8.2 ~ 45-45-90 Triangles

Front

What is a 45-45-90 triangle?

Back

A 45-45-90 triangle is an isosceles right triangle where the angles are 45 degrees, 45 degrees, and 90 degrees.

Front

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

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is equal to the length of a leg multiplied by the square root of 2.

Front

If the length of each leg of a 45-45-90 triangle is 15, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 15√2.

Front

How do you find the length of a leg in a 45-45-90 triangle if the hypotenuse is known?

Back

To find the length of a leg, divide the length of the hypotenuse by √2.

Front

What is the formula for the area of a 45-45-90 triangle?

Back

The area of a 45-45-90 triangle is (1/2) * leg^2.

Front

What is the value of x in a 45-45-90 triangle if the hypotenuse is 20?

Back

x = 20/√2 = 10√2.

Front

What is the significance of the 45-45-90 triangle in real-world applications?

Back

45-45-90 triangles are often used in construction, design, and various fields of engineering due to their predictable properties.

Front

How can you derive the Pythagorean theorem using a 45-45-90 triangle?

Back

In a 45-45-90 triangle, if each leg is 'a', then by the Pythagorean theorem: a^2 + a^2 = (a√2)^2.

Front

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

Back

The angles in a 45-45-90 triangle are complementary, adding up to 90 degrees, with two angles being equal.

Front

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

Back

The hypotenuse is 12√2.