SOH-CAH-TOA and Pythagorean Theorem

Front

What does SOH-CAH-TOA stand for?

Back

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

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It is expressed as: a² + b² = c².

Front

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

Back

The tangent of an angle is calculated by dividing the length of the opposite side by the length of the adjacent side: Tan(θ) = Opposite/Adjacent.

Front

What is the sine of angle A if the opposite side is 10 and the hypotenuse is 20?

Back

Sine A = Opposite/Hypotenuse = 10/20 = 1/2.

Front

What is the cosine of angle B if the adjacent side is 10 and the hypotenuse is 20?

Back

Cosine B = Adjacent/Hypotenuse = 10/20 = 1/2.

Front

If the lengths of the two legs of a right triangle are 3 and 4, what is the length of the hypotenuse?

Back

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

Front

What is the simplified form of √50?

Back

√50 can be simplified to 5√2.

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 using the tangent function?

Back

To find the angle, use the inverse tangent function: θ = tan⁻¹(Opposite/Adjacent).

Front

What is the value of cos⁻¹(0.5)?

Back

cos⁻¹(0.5) = 60° or π/3 radians.