Using Trig to find Missing Angles and Sides

Front

What is the sine ratio in a right triangle?

Back

The sine ratio is defined as the ratio of the length of the opposite side to the length of the hypotenuse. It is expressed as: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$.

Front

What is the cosine ratio in a right triangle?

Back

The cosine ratio is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. It is expressed as: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$.

Front

What is the tangent ratio in a right triangle?

Back

The tangent ratio is defined as the ratio of the length of the opposite side to the length of the adjacent side. It is expressed as: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$.

Front

How do you find the measure of an angle using sine?

Back

To find the measure of an angle using sine, use the inverse sine function: $$\theta = \sin^{-1}\left(\frac{\text{opposite}}{\text{hypotenuse}}\right)$$.

Front

How do you find the measure of an angle using cosine?

Back

To find the measure of an angle using cosine, use the inverse cosine function: $$\theta = \cos^{-1}\left(\frac{\text{adjacent}}{\text{hypotenuse}}\right)$$.

Front

How do you find the measure of an angle using tangent?

Back

To find the measure of an angle using tangent, use the inverse tangent function: $$\theta = \tan^{-1}\left(\frac{\text{opposite}}{\text{adjacent}}\right)$$.

Front

What is the formula for finding a missing side using sine?

Back

To find a missing side using sine, rearrange the sine ratio: $$\text{opposite} = \sin(\theta) \times \text{hypotenuse}$$.

Front

What is the formula for finding a missing side using cosine?

Back

To find a missing side using cosine, rearrange the cosine ratio: $$\text{adjacent} = \cos(\theta) \times \text{hypotenuse}$$.

Front

What is the formula for finding a missing side using tangent?

Back

To find a missing side using tangent, rearrange the tangent ratio: $$\text{opposite} = \tan(\theta) \times \text{adjacent}$$.

Front

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

Back

Using the sine ratio: $$\sin(\theta) = \frac{5}{13} \approx 0.3846$$.