Bridge diagonally 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:

$$\begin{gathered} a=89\text{ m } \\ \alpha =12{\displaystyle \frac{30}{60}}=12+{\displaystyle \frac{30}{60}}={\displaystyle \frac{12\cdot 60+30}{60}}={\displaystyle \frac{750}{60}}={\displaystyle \frac{25}{2}}=12.5\text{ ° } \\ \cos \alpha =a:c=89:91.1609=\mathrm{\infty } \\ c=a\mathrm{/}\cos \alpha \mathrm{°}=a\mathrm{/}\cos 12.5\mathrm{°}=89\mathrm{/}\cos 12.5\mathrm{°}=89\mathrm{/}0.976296=91.16088\text{ m } \\ x=c-a=91.1609-89=2.1609\text{ m} \end{gathered}$$

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