Finding Missing Angles Using Trig Ratios

Front

What is the definition of a trigonometric ratio?

Back

A trigonometric ratio is a ratio of the lengths of two sides of a right triangle. The primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan).

Front

What is the sine ratio in a right triangle?

Back

The sine ratio is defined as the length of the opposite side divided by the length of the hypotenuse. (sin θ = opposite/hypotenuse)

Front

What is the cosine ratio in a right triangle?

Back

The cosine ratio is defined as the length of the adjacent side divided by the length of the hypotenuse. (cos θ = adjacent/hypotenuse)

Front

What is the tangent ratio in a right triangle?

Back

The tangent ratio is defined as the length of the opposite side divided by the length of the adjacent side. (tan θ = opposite/adjacent)

Front

How do you find the missing angle using the tangent ratio?

Back

To find the missing angle using the tangent ratio, use the formula θ = tan^-1(opposite/adjacent).

Front

If the opposite side is 12 and the adjacent side is 29, what is the angle θ?

Back

θ = tan^-1(12/29) which approximately equals 22.6°.

Front

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

Back

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

Front

How do you calculate the measure of an angle if you know the sine ratio?

Back

To calculate the measure of an angle using the sine ratio, use θ = sin^-1(opposite/hypotenuse).

Front

What is the value of m∠ B if tan B = 12/29?

Back

m∠ B = tan^-1(12/29) which is approximately 22.6°.

Front

If m∠ A = 67°, what is m∠ C in a right triangle?

Back

m∠ C = 90° - m∠ A = 90° - 67° = 23°.