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).

Tags

CCSS.HSG.SRT.C.6

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)

Tags

CCSS.HSG.SRT.C.6

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)

Tags

CCSS.HSG.SRT.C.6

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)

Tags

CCSS.HSG.SRT.C.6

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).

Tags

CCSS.HSG.SRT.C.8

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°.

Tags

CCSS.HSG.SRT.C.8

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°.

Tags

CCSS.8.G.A.5

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).

Tags

CCSS.HSG.SRT.C.8

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°.

Tags

CCSS.HSG.SRT.C.8

Front

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

Back

m∠ C = 90° - m∠ A = 90° - 67° = 23°.

Tags

CCSS.7.G.B.5