Shooter

The shooter fired at a target from a distance 49 m. The individual concentric circle of targets has radius increments of 1 cm (25 points) by 1 point. The shot was shifted by 16' (angle degree minutes).

How many points should he win his shot?

Correct answer:

n =  3

Step-by-step explanation:

$$\begin{gathered} x=49\text{m}\to \text{cm}=49\cdot 100\text{cm}=4900\text{cm} \\ \alpha =0°16^{\prime }=0°+\frac{16}{60}°=0.2667°\doteq 0.2667 \\ \tan \alpha =r:x \\ r=x\cdot \tan \alpha =x\cdot \tan 0.26666666666667°=4900\cdot \tan 0.26666666666667°=4900\cdot 0.004654=22.8058\text{cm} \\ R=\lfloor r\rfloor =\lfloor 22.8058\rfloor =22\text{cm} \\ n=25-R=25-22=3 \end{gathered}$$

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