Right Triangles and Trig Review

Front

What is the Pythagorean Theorem?

Back

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.

Tags

CCSS.8.G.B.8

Front

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

Back

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.8

Front

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

Back

Area = 1/2 * base * height.

Tags

CCSS.6.G.A.1

Front

What is the definition of sine in a right triangle?

Back

Sine (sin) is the ratio of the length of the opposite side to the length of the hypotenuse. Formula: sin(θ) = opposite/hypotenuse.

Tags

CCSS.HSG.SRT.C.6

Front

What is the definition of cosine in a right triangle?

Back

Cosine (cos) is the ratio of the length of the adjacent side to the length of the hypotenuse. Formula: cos(θ) = adjacent/hypotenuse.

Tags

CCSS.HSG.SRT.C.6

Front

What is the definition of tangent in a right triangle?

Back

Tangent (tan) is the ratio of the length of the opposite side to the length of the adjacent side. Formula: tan(θ) = opposite/adjacent.

Tags

CCSS.HSG.SRT.C.6

Front

How do you calculate the height of an object using angles of elevation?

Back

Use the formula: height = distance * tan(angle of elevation).

Tags

CCSS.HSG.SRT.C.8

Front

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

Back

The sum of the angles in a right triangle is always 180 degrees, with one angle being 90 degrees.

Tags

CCSS.8.G.A.5

Front

If one angle in a right triangle is 30 degrees, what are the other two angles?

Back

The other two angles must be 60 degrees and 90 degrees, since the sum must equal 180 degrees.

Tags

CCSS.7.G.B.5

Front

What is the length of the diagonal of a rectangle with width 8 inches and height 11 inches?

Back

Using the Pythagorean theorem: diagonal = √(8² + 11²) = √(64 + 121) = √185 ≈ 13.6 inches.

Tags

CCSS.8.G.B.8