Right Triangles

Front

What is a right triangle?

Back

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

Tags

CCSS.4.G.A.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): c² = a² + b².

Tags

CCSS.8.G.B.7

Front

What are the side lengths 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 shortest side is opposite the 30-degree angle, the longer leg is opposite the 60-degree angle, and the hypotenuse is opposite the right angle.

Tags

CCSS.HSG.CO.C.10

Front

What are the side lengths 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.

Tags

CCSS.8.G.B.8

Front

How do you find the length of the hypotenuse in a right triangle?

Back

To find the length of the hypotenuse, use the Pythagorean theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

Tags

CCSS.8.G.B.7

Front

How do you find the length of a missing side in a right triangle?

Back

Use the Pythagorean theorem. If you know the lengths of two sides, rearrange the formula to solve for the missing side.

Tags

CCSS.8.G.B.7

Front

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

Back

The side opposite the largest angle is the longest side (hypotenuse), and the side opposite the smallest angle is the shortest side.

Tags

CCSS.HSG.CO.C.10

Front

What is the formula for the area of a right triangle?

Back

The area of a right triangle is given by the formula: Area = (1/2) × base × height.

Tags

CCSS.6.G.A.1

Front

How do you calculate the diagonal of a rectangle using right triangles?

Back

The diagonal can be calculated using the Pythagorean theorem: d = √(length² + width²), where d is the diagonal.

Tags

CCSS.8.G.B.8

Front

What is the sine function in relation to a right triangle?

Back

In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse: sin(θ) = opposite/hypotenuse.

Tags

CCSS.HSG.SRT.C.6