Tangent Ratio

Front

What is the tangent ratio?

Back

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

Tags

CCSS.HSG.SRT.C.6

Front

How do you calculate the tangent of an angle?

Back

To calculate the tangent of an angle, use the formula: \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \). You can also use a scientific calculator to find \( \tan(\theta) \) directly.

Tags

CCSS.HSG.SRT.C.6

Front

What is the value of \( \tan(45^\circ) \)?

Back

The value of \( \tan(45^\circ) \) is 1, since the opposite and adjacent sides are equal.

Tags

CCSS.HSG.SRT.C.7

Front

If the opposite side is 10 and the adjacent side is 5, what is \( \tan(\theta) \)?

Back

\( \tan(\theta) = \frac{10}{5} = 2 \)

Tags

CCSS.HSG.SRT.C.6

Front

What is the relationship between tangent and the sides of a right triangle?

Back

In a right triangle, the tangent of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Tags

CCSS.HSG.SRT.C.6

Front

How can you find the length of the opposite side using the tangent ratio?

Back

To find the length of the opposite side, use the formula: \( \text{opposite} = \tan(\theta) \times \text{adjacent} \)

Tags

CCSS.HSG.SRT.C.8

Front

What is the tangent of 30 degrees?

Back

The value of \( \tan(30^\circ) \) is \( \frac{1}{\sqrt{3}} \) or approximately 0.577.

Tags

CCSS.HSG.SRT.C.7

Front

What is the tangent of 60 degrees?

Back

The value of \( \tan(60^\circ) \) is \( \sqrt{3} \) or approximately 1.732.

Tags

CCSS.HSG.SRT.C.7

Front

If \( \tan(\theta) = 3 \), what is the ratio of the opposite side to the adjacent side?

Back

The ratio of the opposite side to the adjacent side is 3:1.

Tags

CCSS.HSG.SRT.C.6

Front

How do you solve for an angle using the tangent ratio?

Back

To solve for an angle, use the inverse tangent function: \( \theta = \tan^{-1}(\frac{\text{opposite}}{\text{adjacent}}) \)

Tags

CCSS.HSG.SRT.C.8