Length, Right Triangles Part 2

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

Front

What are the properties of a right triangle?

Back

A right triangle has one angle that measures 90 degrees. The side opposite the right angle is called the hypotenuse, and the other two sides are referred to as the legs.

Front

How do you calculate the length of a side in a right triangle using the Pythagorean theorem?

Back

To find the length of a side, rearrange the Pythagorean theorem formula. For example, to find the length of side a, use: a = √(c² - b²) if c is the hypotenuse and b is the other leg.

Front

What is the relationship between the angles and sides in a right triangle?

Back

In a right triangle, the side opposite the largest angle is the longest side (the hypotenuse), and the side opposite the smallest angle is the shortest side.

Front

What is the definition of a hypotenuse?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

What is the definition of the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle.

Front

How can you determine if a triangle is a right triangle?

Back

A triangle is a right triangle if it satisfies the Pythagorean theorem: a² + b² = c², where c is the length of the longest side.

Front

What is the concept of similar triangles?

Back

Similar triangles have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

How do you apply the concept of similar triangles to solve problems?

Back

To solve problems using similar triangles, set up a proportion between the lengths of corresponding sides and use cross-multiplication to find unknown lengths.

Front

What is the definition of the sine function in a right triangle?

Back

The sine function (sin) of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse: sin(θ) = opposite/hypotenuse.