5.4 Using Soh Cah Toa to find missing sides

Front

What does Soh Cah Toa stand for?

Back

Soh Cah Toa 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 find the sine of an angle in a right triangle?

Back

To find the sine of an angle, divide the length of the side opposite the angle by the length of the hypotenuse.

Front

If the opposite side is 5 and the hypotenuse is 13, what is the sine of the angle?

Back

Sine = Opposite/Hypotenuse = 5/13 ≈ 0.3846.

Front

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

Back

Cosine is the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

If the adjacent side is 12 and the hypotenuse is 13, what is the cosine of the angle?

Back

Cosine = Adjacent/Hypotenuse = 12/13 ≈ 0.9231.

Front

How do you find the tangent of an angle in 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 5 and the adjacent side is 12, what is the tangent of the angle?

Back

Tangent = Opposite/Adjacent = 5/12 ≈ 0.4167.

Front

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

Back

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: a² + b² = c².

Front

If one side is 3 and the other side is 4, what is the length of the hypotenuse?

Back

Using the Pythagorean theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the sine of a 30-degree angle?

Back

Sine(30°) = 1/2.