The points A, B, and C form a triangle.
From the given information in the question, the triangle ABC can be drawn to have the following parameters:
Recall the Sine Rule. Applied to the triangle above, the rule is stated as follows:
[tex]\frac{BC}{\sin A}=\frac{AC}{\sin B}=\frac{AB}{\sin C}[/tex]
The length of the bridge is AB. Given that the measures of angles A and C, and side BC are known, the following ratio is used to solve:
[tex]\frac{BC}{\sin A}=\frac{AB}{\sin C}[/tex]
Substituting known values, the length of AB is calculated as follows:
[tex]\begin{gathered} \frac{62}{\sin80}=\frac{AB}{\sin60} \\ AB=\frac{62\times\sin60}{\sin80} \\ AB=54.52 \end{gathered}[/tex]
The bridge is 54.52 m long.
