9.2 special right triangles

Front

What is a 30-60-90 triangle?

Back

A special right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. The sides are in the ratio 1:√3:2.

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are both 45 degrees and the sides are in the ratio 1:1:√2.

Front

How do you find the lengths of the sides in a 30-60-90 triangle?

Back

The length of the side opposite the 30-degree angle is x, the side opposite the 60-degree angle is x√3, and the hypotenuse is 2x.

Front

How do you find the lengths of the sides in a 45-45-90 triangle?

Back

The lengths of the legs are equal, and the hypotenuse is the leg length multiplied by √2.

Front

What is the formula for the sine of an angle in a right triangle?

Back

Sine = opposite side / hypotenuse.

Front

What is the formula for the cosine of an angle in a right triangle?

Back

Cosine = adjacent side / hypotenuse.

Front

What is the formula for the tangent of an angle in a right triangle?

Back

Tangent = opposite side / adjacent side.

Front

How do you calculate the length of a ramp given the height and angle of inclination?

Back

Use the formula: length = height / sin(angle).

Front

If the height of a ramp is 4 inches and the angle is 10 degrees, how do you estimate the length of the ramp?

Back

Length = 4 / sin(10°) ≈ 22.7 inches.

Front

What is the relationship between the length of a ladder and its distance from the wall?

Back

If the length of the ladder is one foot more than twice its distance from the wall, use the equation: length = 2(distance) + 1.