SOHCAHTOA

Front

What does SOHCAHTOA stand for in trigonometry?

Back

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

Front

How do you calculate the sine of an angle in a right triangle?

Back

The sine of an angle is calculated by dividing the length of the side opposite the angle by the length of the hypotenuse.

Front

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

Back

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

Define tangent in the context of a right triangle.

Back

Tangent is the ratio of the length of the opposite side to the length of the adjacent side.

Front

If the opposite side is 6 and the hypotenuse is 10, what is the sine of the angle?

Back

Sine = Opposite/Hypotenuse = 6/10 = 0.6.

Front

What is the formula to find the height of an object using trigonometry?

Back

Height = Distance from the object * tan(angle).

Front

How can you use SOHCAHTOA to find an unknown side in a right triangle?

Back

Identify which sides you know (opposite, adjacent, hypotenuse) and which angle you have, then use the appropriate trigonometric ratio (sine, cosine, or tangent) to solve for the unknown side.

Front

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

Back

In a right triangle, the angles determine the ratios of the lengths of the sides, which can be expressed using sine, cosine, and tangent.

Front

How do you find the angle if you know two sides of a right triangle?

Back

You can use the inverse trigonometric functions: angle = sin^(-1)(opposite/hypotenuse), cos^(-1)(adjacent/hypotenuse), or tan^(-1)(opposite/adjacent).

Front

What is the height of a tree if the distance from the observer is 50 ft and the angle of elevation is 30 degrees?

Back

Height = 50 * tan(30 degrees) = 50 * (1/sqrt(3)) ≈ 28.87 ft.