Question

斜率为 $2$ 和 $\tfrac13$ 的两条直线所成锐角的度数是多少？

What is the degree measure of the acute angle formed by lines with slopes $2$ and $\tfrac13?$

$30$

$37.5$

$45$

$52.5$

$60$

两直线夹角的正切为 $\left|\dfrac{2-\tfrac13}{1+2\cdot\tfrac13}\right| =\left|\dfrac{\tfrac53}{\tfrac53}\right|=1.$

正切为 $1$ 的锐角是 $45^\circ$ 。

所以正确答案是 C。

The tangent of the angle between the lines is $\left|\dfrac{2-\tfrac13}{1+2\cdot\tfrac13}\right| =\left|\dfrac{\tfrac53}{\tfrac53}\right|=1.$

The acute angle with tangent $1$ is $45^\circ.$

Thus, the correct answer is C.