Missing Leg: Pythagorean Theorem

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). Formula: a² + b² = c².

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What is the hypotenuse in a right triangle?

Back

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

Front

If one leg of a right triangle is 3 m and the other leg is 4 m, what is the length of the hypotenuse?

Back

5 m (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

What is the formula to find the length of a missing leg in a right triangle?

Back

To find a missing leg (a or b), use the formula: a² = c² - b² or b² = c² - a².

Front

Can the legs of a right triangle be equal?

Back

Yes, if the legs are equal, the triangle is an isosceles right triangle.

Front

What is the relationship between the legs and the hypotenuse in a right triangle?

Back

The lengths of the legs must always be shorter than the length of the hypotenuse.

Front

If the hypotenuse is 10 m and one leg is 6 m, what is the length of the other leg?

Back

8 m (Using the Pythagorean Theorem: 10² = 6² + b²; 100 = 36 + b²; b² = 64; b = 8).

Front

What is the significance of the Pythagorean Theorem in real life?

Back

It is used in various fields such as construction, navigation, and physics to calculate distances and angles.

Front

What is the value of x if a right triangle has legs of 5 in and x in, and a hypotenuse of 13 in?

Back

12 in (Using the Pythagorean Theorem: 5² + x² = 13²; 25 + x² = 169; x² = 144; x = 12).