Geometry - Solving Right Triangles

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

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): c² = a² + b².

Front

What are the three sides of a right triangle called?

Back

The three sides of a right triangle are called the hypotenuse (the longest side), the opposite side (the side opposite the angle of interest), and the adjacent side (the side next to the angle of interest).

Front

What are trigonometric ratios?

Back

Trigonometric ratios are relationships between the angles and sides of a right triangle, specifically sine (sin), cosine (cos), and tangent (tan).

Front

What does SOH CAH TOA stand for?

Back

SOH CAH TOA is a mnemonic to remember the definitions of sine, cosine, and tangent: SOH = Sine = Opposite/Hypotenuse, CAH = Cosine = Adjacent/Hypotenuse, TOA = Tangent = Opposite/Adjacent.

Front

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

Back

The sine of an angle is found by dividing the length of the opposite side by the length of the hypotenuse: sin(θ) = opposite/hypotenuse.

Front

How do you find the cosine of an angle in a right triangle?

Back

The cosine of an angle is found by dividing the length of the adjacent side by the length of the hypotenuse: cos(θ) = adjacent/hypotenuse.

Front

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

Back

The tangent of an angle is found by dividing the length of the opposite side by the length of the adjacent side: tan(θ) = opposite/adjacent.

Front

What is an inverse trigonometric function?

Back

Inverse trigonometric functions are used to find the angle when the values of the sides are known. They include arcsin, arccos, and arctan.

Front

How do you use inverse trigonometric functions to find a missing angle?

Back

To find a missing angle, use the appropriate inverse trigonometric function based on the known sides. For example, if you know the opposite and hypotenuse, use arcsin.