Special Right Triangles and Trig Ratios

Front

What is a special right triangle?

Back

A special right triangle is a right triangle with specific angle measures that allow for easy calculation of side lengths. The two main types are the 30-60-90 triangle and the 45-45-90 triangle.

Tags

CCSS.HSG.CO.C.10

Front

What are the side ratios of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the side lengths are in the ratio 1 : √3 : 2, where 1 is the length of the side opposite the 30° angle, √3 is the length of the side opposite the 60° angle, and 2 is the length of the hypotenuse.

Tags

CCSS.HSG.CO.C.10

Front

What are the side ratios of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the side lengths are in the ratio 1 : 1 : √2, where 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 a side in a 30-60-90 triangle?

Back

To find the length of a side in a 30-60-90 triangle, use the ratios: if the shortest side (opposite the 30° angle) is x, then the side opposite the 60° angle is x√3, and the hypotenuse is 2x.

Tags

CCSS.8.G.B.8

Front

How do you find the length of a side in a 45-45-90 triangle?

Back

In a 45-45-90 triangle, if the length of each leg is x, then the hypotenuse is x√2.

Tags

CCSS.8.G.B.8

Front

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

Back

The sine function (sin) is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.

Tags

CCSS.HSG.SRT.C.6

Front

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

Back

The cosine function (cos) is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.

Tags

CCSS.HSG.SRT.C.6

Front

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

Back

The tangent function (tan) is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side.

Tags

CCSS.HSG.SRT.C.6

Front

How do you use sine to find a side length?

Back

To find a side length using sine, use the formula: sin(angle) = opposite/hypotenuse. Rearranging gives opposite = hypotenuse * sin(angle).

Tags

CCSS.HSG.SRT.C.8

Front

How do you use cosine to find a side length?

Back

To find a side length using cosine, use the formula: cos(angle) = adjacent/hypotenuse. Rearranging gives adjacent = hypotenuse * cos(angle).

Tags

CCSS.HSG.SRT.C.8