Trigonometric Ratios in 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 are the three sides of a right triangle called?

Back

The three sides are called the hypotenuse (the longest side), the opposite side (opposite the angle of interest), and the adjacent side (next to the angle of interest).

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

What is the sine ratio?

Back

The sine ratio is defined as 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

Front

What is the cosine ratio?

Back

The cosine ratio is defined as the ratio of the length of the adjacent side to the length of the hypotenuse: cos(θ) = adjacent/hypotenuse.

Tags

CCSS.HSG.SRT.C.6

Front

What is the tangent ratio?

Back

The tangent ratio is defined as the ratio of the length of the opposite side to the length of the adjacent side: tan(θ) = opposite/adjacent.

Tags

CCSS.HSG.SRT.C.6

Front

How do you find the length of the hypotenuse using trigonometric ratios?

Back

To find the hypotenuse, use the sine or cosine ratio: hypotenuse = opposite/sin(θ) or hypotenuse = adjacent/cos(θ).

Tags

CCSS.HSG.SRT.C.8

Front

How do you find the length of a side using the tangent ratio?

Back

To find the length of a side, use the tangent ratio: opposite = adjacent * tan(θ) or adjacent = opposite/tan(θ).

Tags

CCSS.HSG.SRT.C.8

Front

What is the relationship between the sine and cosine of complementary angles?

Back

The sine of an angle is equal to the cosine of its complementary angle: sin(θ) = cos(90° - θ).

Tags

CCSS.HSG.SRT.C.7

Front

What is the value of sin(30°)?

Back

The value of sin(30°) is 0.5.

Tags

CCSS.HSG.SRT.C.7