Pythagorean Theorem all sides

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

If a = 3 and b = 4, what is c?

Back

c = 5 (Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25, thus c = √25 = 5).

Front

What is the length of side c if a = 5 and b = 12?

Back

c = 13 (Using the Pythagorean Theorem: c² = 5² + 12² = 25 + 144 = 169, thus c = √169 = 13).

Front

If c = 10 and a = 6, what is b?

Back

b = 8 (Using the Pythagorean Theorem: 10² = 6² + b², thus 100 = 36 + b², so b² = 64, thus b = √64 = 8).

Front

What is the length of side a if b = 8 and c = 10?

Back

a = 6 (Using the Pythagorean Theorem: 10² = a² + 8², thus 100 = a² + 64, so a² = 36, thus a = √36 = 6).

Front

In a right triangle, if one angle is 90 degrees, what are the other two angles?

Back

The other two angles must add up to 90 degrees, as the sum of angles in a triangle is always 180 degrees.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The side opposite the 30-degree angle is the shortest.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, it is a right triangle (Using the Pythagorean Theorem: 25² = 7² + 24², thus 625 = 49 + 576 = 625).

Front

What is the formula to find the area of a right triangle?

Back

Area = (1/2) * base * height.