Trig Ratios: SOHCAHTOA

Front

What does SOHCAHTOA stand for?

Back

SOHCAHTOA is a mnemonic for remembering the definitions of the sine, cosine, and tangent ratios in a right triangle: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.

Front

How do you calculate the length of a shadow using trigonometric ratios?

Back

To calculate the length of a shadow, use the tangent ratio: Tan(angle) = Opposite (height of the object) / Adjacent (length of the shadow). Rearranging gives: Length of shadow = Height of object / Tan(angle).

Front

If a right triangle has an angle of 30 degrees and the length of the opposite side is 5 ft, what is the length of the hypotenuse?

Back

Using the sine ratio: Sin(30) = Opposite/Hypotenuse. Therefore, Hypotenuse = Opposite/Sin(30) = 5/Sin(30) = 10 ft.

Front

What is the cosine of a 45-degree angle?

Back

The cosine of a 45-degree angle is √2/2 or approximately 0.707.

Front

In a right triangle, if the adjacent side is 8 ft and the angle is 60 degrees, what is the length of the opposite side?

Back

Using the tangent ratio: Tan(60) = Opposite/Adjacent. Therefore, Opposite = Adjacent * Tan(60) = 8 * √3 ≈ 13.9 ft.

Front

What is the relationship between the sides of a right triangle and the angles?

Back

The lengths of the sides of a right triangle are proportional to the sine, cosine, and tangent of its angles.

Front

How do you find the height of an object using trigonometry?

Back

To find the height of an object, use the sine ratio: Height = Hypotenuse * Sin(angle).

Front

If a ladder is 20 ft long and makes a 30-degree angle with the ground, how high does it reach on the wall?

Back

Using the sine ratio: Height = Hypotenuse * Sin(30) = 20 * 0.5 = 10 ft.

Front

What is the tangent of a 45-degree angle?

Back

The tangent of a 45-degree angle is 1.

Front

If the height of a building is 50 ft and the angle of elevation to the top of the building from a point 30 ft away is needed, how do you find the angle?

Back

Use the tangent ratio: Tan(angle) = Opposite/Adjacent = 50/30. Therefore, angle = arctan(50/30).