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 \( \tan(30\degree) \)?

Back

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

Tags

CCSS.HSG.SRT.C.7

Front

What is the value of \( \tan(35\degree) \)?

Back

The value of \( \tan(35\degree) \) is approximately 0.700.

Tags

CCSS.HSG.SRT.C.7

Front

If the opposite side is 14 and the angle is 35 degrees, how do you find the adjacent side?

Back

Use the tangent ratio: \( \tan(35\degree) = \frac{14}{\text{adjacent}} \). Rearranging gives: \( \text{adjacent} = \frac{14}{\tan(35\degree)} \).

Tags

CCSS.HSG.SRT.C.8

Front

What is the formula to find the opposite side using the tangent ratio?

Back

The formula to find the opposite side is: \( \text{opposite} = \tan(\theta) \times \text{adjacent} \).

Tags

CCSS.HSG.SRT.C.8

Front

How do you find the missing variable in a tangent ratio problem?

Back

Identify the known sides and angle, then use the tangent ratio formula to solve for the missing side.

Tags

CCSS.HSG.SRT.C.8

Front

What is the approximate value of \( \tan(47\degree) \)?

Back

The approximate value of \( \tan(47\degree) \) is 1.072.

Tags

CCSS.HSG.SRT.C.7

Front

If the adjacent side is 30 and the angle is C, how do you find the opposite side?

Back

Use the tangent ratio: \( \tan(C) = \frac{\text{opposite}}{30} \). Rearranging gives: \( \text{opposite} = 30 \cdot \tan(C) \).

Tags

CCSS.HSG.SRT.C.8

Front

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

Back

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

Tags

CCSS.HSG.SRT.C.6