Question

What is tan C?

O
11
이
B
Express your answer as a simplified fraction.
0f
22

Answer 1

Explanation:

`\tan = (opposite)/(adjacent) \\ = (11)/(22) \\ = (1)/(2)`

Answer 2

`(1)/(2)`

Explanation:

The tangent trigonometric ratio relates the angle of a right triangle to the ratio of the length of the side opposite that angle to the length of the side adjacent to it.

`\boxed{\begin{array}{l}\underline{\textsf{Tangent trigonometric ratio}}\\\\\sf \tan(\theta)=(O)/(A)\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$\theta$ is the angle.}\\\phantom{ww}\bullet\;\textsf{$O$ is the side opposite the angle.}\\\phantom{ww}\bullet\;\textsf{$A$ is the side adjacent the angle.}\end{array}}`

In the given right triangle, the side opposite angle C is 11 units and the side adjacent angle C is 22 units. Therefore:

• θ = C
• O = 11
• A = 22

Substitute these values into the tangent ratio:

`\tan C=(11)/(22)`

Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 11:

`\tan C=(11/ 11)/(22/ 11)=(1)/(2)`

Therefore, the value of tan C as a simplified fraction is ¹/₂.