Question

1. kayak a and kayak b leave a dock as shown. which kayak is closer to the dock?

Explanation:

Step1: Define distance to dock

We need to find the perpendicular distance (let's call it $d$) from each kayak to the dock, which is the shortest distance. For a triangle with side length $L$, angle $\theta$ between the side and the dock, the perpendicular distance is $d = L\sin\theta$.

Step2: Calculate distance for Kayak A

Kayak A: $L=120$ yd, $\theta=50^\circ$
$d_A = 120\sin(50^\circ)$
$\sin(50^\circ)\approx0.7660$, so $d_A\approx120\times0.7660=91.92$ yd

Step3: Calculate distance for Kayak B

Kayak B: $L=120$ yd, $\theta=45^\circ$
$d_B = 120\sin(45^\circ)$
$\sin(45^\circ)=\frac{\sqrt{2}}{2}\approx0.7071$, so $d_B\approx120\times0.7071=84.85$ yd

Step4: Compare the two distances

Since $84.85 < 91.92$, Kayak B is closer.

Answer:

Kayak B is closer to the dock.