From the top of a 210 - ft lighthouse, the angle of depression to a ship in the ocean is \( 16^{\circ} \). How far is the ship from the base of the lighthouse? distance \( \approx \) Report answer accurate to 1 decimal place.

To find the distance of the ship from the base of the lighthouse, we can use the tangent function in trigonometry. Given: - Height of the lighthouse = 210 ft - Angle of depression = \( 16^{\circ} \) We can use the tangent function to find the distance of the ship from the base of the lighthouse: \[ \tan(\text{angle of depression}) = \frac{\text{opposite side}}{\text{adjacent side}} \] In this case, the opposite side is the height of the lighthouse (210 ft) and the adjacent side is the distance of the ship from the base of the lighthouse. Let's denote the distance of the ship from the base of the lighthouse as \( x \). Using the tangent function: \[ \tan(16^{\circ}) = \frac{210}{x} \] Now, we can solve for \( x \) to find the distance of the ship from the base of the lighthouse. Calculate the value by following steps: - step0: Calculate: \(\frac{210}{\tan\left(16\right)}\) - step1: Calculate the trigonometric value: \(698.527871\) The distance of the ship from the base of the lighthouse is approximately 698.5 ft.