Right Triangle Trigonometry

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 is the sine ratio?

Back

The sine ratio (sin) is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle: sin(θ) = Opp/Hyp.

Tags

CCSS.HSG.SRT.C.6

Front

What is the cosine ratio?

Back

The cosine ratio (cos) is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle: cos(θ) = Adj/Hyp.

Tags

CCSS.HSG.SRT.C.6

Front

What is the tangent ratio?

Back

The tangent ratio (tan) is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle: tan(θ) = Opp/Adj.

Tags

CCSS.HSG.SRT.C.6

Front

How do you find the length of a side using sine?

Back

To find the length of a side using sine, use the formula: sin(θ) = Opp/Hyp, and rearrange to find Opp = Hyp * sin(θ).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

How do you find the length of a side using cosine?

Back

To find the length of a side using cosine, use the formula: cos(θ) = Adj/Hyp, and rearrange to find Adj = Hyp * cos(θ).

Tags

CCSS.HSG.SRT.C.8

Front

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

Back

To find the length of a side using tangent, use the formula: tan(θ) = Opp/Adj, and rearrange to find Opp = Adj * tan(θ).

Tags

CCSS.HSG.SRT.C.8

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.

Tags

CCSS.HSG.CO.C.10

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 length of the hypotenuse is √2 times the length of each leg.

Tags

CCSS.8.G.B.8