Question

find the Slope of a line whose inclination is 15 degrees​

Answer 1

Answer:

Slope of line is 0.26

Step-by-step explanation:

Slope = TanA

A = 15°

Tan 15° = 0.26

Answer 2

The slope of the a line whose inclination is 15 degrees​ is $2-\sqrt{3}$ .

Step-by-step explanation:

To find : Slope of a line whose inclination is 15 degrees​.

We assume that the the line is inclined to positive x -axis.

We know that the slope of the line whose inclination is $\theta$ is $tan \theta$.

Then, the slope the line whose inclination is 15 degrees​ will be $\tan(15^{\circ})=\tan(45^{\circ}-30^{\circ})\\\\=\dfrac{\tan(45^{\circ})-\tan(30^{\circ})}{1+\tan(45^{\circ}\tan(30^{\circ})}\ \ [\because\ \tan{A-B}=\dfrac{\tan A-\tan B}{1+\tan A+\tan B}]\\\\=\dfrac{1-\dfrac{1}{\sqrt{3}}}{1+(1)(\dfrac{1}{\sqrt{3}})}\\\\=\dfrac{\dfrac{\sqrt{3}-1}{\sqrt{3}}}{\dfrac{\sqrt{3}+1}{\sqrt{3}}}\\\\=\dfrac{\sqrt{3}-1}{\sqrt{3}+1}\times\dfrac{\sqrt{3}-1}{\sqrt{3}-1}\\\\=\dfrac{(\sqrt{3}-1)^2}{3-1}\\\\=\dfrac{3+1-2\sqrt{3}}{2}=2-\sqrt{3}$

Hence, the slope of the a line whose inclination is 15 degrees​ is $2-\sqrt{3}$ .

# Learn more :

Find the slope of the line whose inclination is 60°

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