Question

In a right triangle, the side opposite angle θ has a length of 80 inches, the side adjacent to angle θ has a length of 84 inches, and the hypotenuse has a length of 116 inches. What is the value of tan(θ)?

Answer 1

The sides of a right triangle are hypotenuse, opposite, and adjacent.

The hypotenuse is the longest sides of the triangle.

The opposite is the side facing the angle.

The adjacent is the third side of the right triangle.

This sides are illustrated as shown below:

Thus, in the above right triangle ABC,

`\begin{gathered} AC\Rightarrow hypotenuse \\ AB\Rightarrow opposite \\ BC\Rightarrow adjacent \end{gathered}`

Given that the opposite side has a length of 80 inches, adjacent has a length of 84 inches, and the hypotenuse has a length of 116 inches, this implies that

`\begin{gathered} AC=116 \\ AB=80 \\ BC=84 \end{gathered}`

To evaluate the value of

`\tan(\theta)`

We use trigonometric ratios.

From trigonometric ratios,

`\tan\theta=(opposite)/(adjacent)`
`\begin{gathered} where \\ opposite\Rightarrow AB=80 \\ adjacent\Rightarrow BC=84 \\ thus, \\ \tan(\theta)=(AB)/(BC)\frac{}{} \\ =(80)/(84)=0.9523809524 \end{gathered}`

Hence, the value of tan (θ) is

`0.952`

The first option is the correct answer.