Brendan was in a boat observing a lighthouse on a vertical cliff at an angle of elevation of \( 54^{\circ} \). The cliff was 94 meters high. Find the horizontal distance from Brendan to the base of the cliff. \( \begin{array}{ll}\text { a) } 56 \mathrm{~m} & \text { go to station } 6 \\ \text { b) } 54 \mathrm{~m} & \text { go to station } 8 \\ \text { c) } 15 \mathrm{~m} & \text { go to station } 2 \\ \text { d) } 68 \mathrm{~m} & \text { go to station } 5 \\ \text { e) } 76 \mathrm{~m} & \text { go to station } 4\end{array} \)

To find the horizontal distance from Brendan to the base of the cliff, we can use the tangent function from trigonometry. The tangent of the angle of elevation (\(54^{\circ}\)) is equal to the height of the cliff (94 m) divided by the horizontal distance (d) from Brendan to the base. Using the formula: \[ \tan(54^{\circ}) = \frac{94}{d} \] We can rearrange this to find \(d\): \[ d = \frac{94}{\tan(54^{\circ})} \] Calculating gives d approximately \(68\) meters. So, the horizontal distance from Brendan to the base of the cliff is \( 68 \, \text{m} \) – option d! Brendan probably needed to steer clear; you can't be too careful near cliffs! It's a great reminder that whether you’re sailing in a boat or just tackling life's challenges, knowing your distances can help you avoid some unexpected pitfalls—especially when they’re as towering as a cliff! So next time you're out on the water, remember to keep an eye out for those angles of elevation; they might just save you from a rocky situation! Exploring trigonometry might even make you the captain of the seas!