Bridge across the river

The width of the river is 89 m. For terrain reasons, the bridge deviates from a common perpendicular to both banks by an angle of 12° 30 '. Calculate how many meters the bridge is longer than the river.

Correct answer:

x =  2.1609 m

Step-by-step explanation:

$$\begin{gathered} a=89\text{m} \\ \alpha =12°30^{\prime }=12°+\frac{30}{60}°=12.5°=12.5 \\ \cos \alpha =a:c \\ c=a/\cos \alpha =a/\cos 12.5°=89/\cos 12.5°=89/0.976296=91.16088\text{m} \\ x=c-a=91.1609-89=2.1609\text{m} \end{gathered}$$

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