Question 86

The slopes of two lines are 1 and $$\frac{1}{\sqrt{3}}$$. What is the angle between these two lines?

Solution

Slope of the two lines, $$m_1=1$$ and $$m_2=\frac{1}{\sqrt{3}}$$

Let angle between them = $$\theta$$

Then, $$tan(\theta)=|\frac{m_1-m_2}{1+m_1m_2}|$$

=> $$tan(\theta) = \frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}$$

=> $$tan(\theta)=\frac{tan(45)-tan(30)}{1+tan(45)tan(30)}$$

=> $$tan(\theta)=tan(45-30)$$ $$\because [tan(A-B)=\frac{tanA-tanB}{1+tanAtanB}]$$

=> $$\theta = 15$$°

=> Ans - (A)

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