SOHCAHTOA Word Problems & Practice

Front

What does SOHCAHTOA stand for?

Back

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

Front

How do you find the length of a side in a right triangle using SOHCAHTOA?

Back

To find a side length, identify the angle and the known side. Use the appropriate trigonometric ratio (sine, cosine, or tangent) to set up an equation and solve for the unknown side.

Front

If the angle is 30° and the hypotenuse is 10, what is the length of the opposite side?

Back

Using SOH (Sine), Opposite = Hypotenuse * sin(30°) = 10 * 0.5 = 5.

Front

What is the formula for finding the cosine of an angle?

Back

Cosine of an angle = Adjacent side / Hypotenuse.

Front

If the adjacent side is 6 and the hypotenuse is 10, what is the cosine of the angle?

Back

Cosine = 6/10 = 0.6.

Front

How do you calculate the tangent of an angle?

Back

Tangent of an angle = Opposite side / Adjacent side.

Front

If the opposite side is 4 and the adjacent side is 3, what is the tangent of the angle?

Back

Tangent = 4/3.

Front

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

Back

In a right triangle, the sum of the angles is always 180°, with one angle being 90°.

Front

How do you find the missing angle in a right triangle if you know the other two angles?

Back

Subtract the sum of the known angles from 90° to find the missing angle.

Front

What is the height of a ladder leaning against a wall if it makes a 65° angle with the ground and reaches 20 feet high?

Back

Use the sine function: Height = Hypotenuse * sin(65°). Hypotenuse can be calculated using the height and angle.