Step 1: Draw the triangle.
Step 2: Concept
Use the trigonometric ratio to find the length of the string.
[tex]\begin{gathered} \sin \theta\text{ = }\frac{opposite}{\text{hypotenuse}} \\ \tan \theta\text{ = }\frac{\text{opposite}}{\text{adjacent}} \\ \cos \theta\text{ = }\frac{adjacent}{\text{hypotenuse}} \end{gathered}[/tex]
Step 3: Name the sides of the triangle
Hypotenuse = L side facing right angle
Opposite = 82 ft side facing given angle
Adjacent = ___ The third side.
Step 4: Apply the sine formula to find the length of the string.
[tex]\begin{gathered} \sin \theta\text{ = }\frac{Opposite}{\text{Hypotenuse}} \\ \sin 61\text{ = }\frac{82}{L} \\ 0.8746\text{ = }\frac{82}{L} \\ \end{gathered}[/tex]
Next, cross multiply
[tex]\begin{gathered} 0.8746L\text{ = 82} \\ \text{Divide through by 0.8746} \\ L\text{ = }\frac{82}{0.8746} \\ L\text{ = 93.8 ft} \end{gathered}[/tex]
Final answer
The length of the string = 93.8 ft
