Question

what would the diagram look like in order for us to use the tangent ratio? 120 miles x 27° dock a

Explanation:

Step1: Recall tangent ratio definition

The tangent of an angle in a right triangle is $\tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}}$. For $\theta=27^\circ$, we need its opposite ($x$) and adjacent sides, plus the hypotenuse (120 miles) labeled.

Step2: Label sides for tangent

• Mark the $27^\circ$ angle at Dock A.
• Label the side opposite $27^\circ$ as $x$ (vertical side).
• Label the adjacent side (horizontal, from Dock A to right angle) as an unknown (e.g., $a$).
• Keep the hypotenuse labeled 120 miles.

Step3: Highlight tangent-relevant sides

Emphasize the $27^\circ$ angle, its opposite side $x$, and adjacent side $a$ to show the tangent ratio applies to these two sides relative to the angle.

Answer:

The diagram must be a right triangle with:

1. The $27^\circ$ angle at Dock A,
2. The vertical side (opposite the $27^\circ$ angle) labeled $x$,
3. The horizontal side (adjacent to the $27^\circ$ angle) labeled as an adjacent unknown length,
4. The hypotenuse (slanted side from Dock A to the top of the vertical side) labeled 120 miles,
5. The right angle symbol clearly shown at the corner of the vertical and horizontal sides.

This setup lets us write $\tan(27^\circ) = \frac{x}{\text{adjacent side}}$ to use the tangent ratio.