Question

a boat is moored at a dock, as shown in the figure.
what is the length of rope a?
note: the triangle formed is a right triangle.
12.3 ft
10.5 ft
8.3 ft
8.6 ft

Explanation:

Step1: Identify trigonometric ratio

In a right triangle, the cosine of an angle is the adjacent side over the hypotenuse. Here, angle is \(35^\circ\), hypotenuse is \(15\) ft, and adjacent side is \(A\). So \(\cos(35^\circ)=\frac{A}{15}\).

Step2: Solve for \(A\)

Rearrange the formula: \(A = 15\times\cos(35^\circ)\). Calculate \(\cos(35^\circ)\approx0.8192\). Then \(A = 15\times0.8192\approx12.3\) ft.

Answer:

12.3 ft