Traffic sign

There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls).

Correct result:

A =  4.0042 °
B =  4.014 °

Solution:

$$\begin{gathered} r=7\mathrm{\%}={\displaystyle \frac{7}{100}}=0.07 \\ \tan A={\displaystyle \frac{y}{x}}=r \\ A={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arctan (r)={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arctan (0.07)=4.0042^{\circ }=4^{\circ }15\mathrm{"} \end{gathered}$$

$$\begin{gathered} r=y\mathrm{/}a \\ a=1\text{ m } \\ {y}_1=a\cdot r=1\cdot 0.07={\displaystyle \frac{7}{100}}=0.07\text{ m } \\ {x}_1=\sqrt{a^2-y_1^2}=\sqrt{1^2-0.07^2}\doteq 0.9975\text{ m } \\ B={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arctan ({\displaystyle \frac{y_1}{x_1}})={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arctan ({\displaystyle \frac{0.07}{0.9975}})\doteq 4.014=4.014^{\circ }=4^{\circ }50\mathrm{"} \\ B\approx A \end{gathered}$$

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