Question

(a) The figure drawn alongside (not drawn
to scale) shows two straight lines AB
and CD. If the equation of line AB is :
x - 3y + 5 = 0 and the equation of line
CD is : x - y = 2; write down the inclinations
of lines AB and CD; also find the angle o
i.e., angle CPB.

plz answer this one!!​

Answer 1

Hello mate,

(Check the above diagram for better understanding)

If we find inclination of line AB, we will get $\alpha$ value as 18.5°

For your understanding, I'll solve this question, and if you have written any mistake in the question, just change the value of $\alpha$ and continue the process Ive done.

Given:

• Line AB => x - 3y + 5 = 0

• Line CD => x - y - 2 = 0

To Find:

• Inclination of line AB and CD

• Value of angle CPB

$\huge{\red{\star}} {\blue{\underline{\huge{\textsf{Solution}}}}} \huge{\red{\star}}$

$we \: \: know \\ \\ \tan( \alpha ) = \frac{ - a}{b}$

For the first line AB,

$\tan( \alpha ) = \frac{ - 1}{ -3} \\ \\ \alpha = 18.5 \: \:degrees \: \: approx$

For the second line CD,

$\tan( \alpha ) = \frac{ - 1}{ - 1} \\ \\ \alpha = 45 \: \: degrees$

As per the above diagram,

MNP is a triangle,

We got:

• Angle(M) = 18.5°

• Angle(N) = 45°

Angle PNM = 180 - 45

= 135°

We know sum of all angles of triangle are equal to 180°,

18.5 + 135 + CPM = 180°

Angle CPM = 26.5°

Now (angle CPB) = 180 - (Angle CPM)

CPB = 180 - 26.5

CPB = 153.5°

If equation of line is different in the actual question then just substitute the angle you have gotten instead of angle M

Then the whole process is the same.

Hope it helps:)