Pyth'n Th'm, Sp Rt Triangles and Trig

Front

What is the definition of 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

How do you calculate the height of an object using its shadow and the angle of elevation?

Back

You can use the tangent function: height = shadow length × tan(angle of elevation).

Tags

CCSS.HSG.SRT.C.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.

Tags

CCSS.HSG.SRT.C.6

Front

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

Back

In a right triangle, the cosine of an angle is 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

In a right triangle, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

Tags

CCSS.HSG.SRT.C.6

Front

How do you find the angle of elevation given the height and shadow length?

Back

You can use the inverse tangent function: angle = arctan(height / shadow length).

Tags

CCSS.HSG.SRT.C.8

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 a leg.

Tags

CCSS.8.G.B.8

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the length of the side opposite the 30-degree angle is half the length of the hypotenuse, and the length of the side opposite the 60-degree angle is √3 times the length of the side opposite the 30-degree angle.

Tags

CCSS.HSG.CO.C.10

Front

How can you estimate the height of an object using similar triangles?

Back

You can set up a proportion based on the corresponding sides of similar triangles to find the unknown height.

Tags

CCSS.HSG.SRT.B.5