## Problem 4.2 Projection of Straight Lines – A line AB, 60 mm long, is inclined at an angle of 45^{0} to HP. and 30^{0} to VP. One of its end point A is in HP as well as VP. Determine its apparent inclinations.

**Procedure: **

**Procedure:**

* Step-1* Draw a horizontal line, which is x-y line of some suitable length.

* Step-2* Mark a point a’ & a on a common point on the x-y line.

* Step-3* Draw a line a’b’

_{1}from the point a’, above & at an angle 45°, which is represented by the letter θ, with the x-y line as shown into the figure.

* Step-4* Draw a line ab

_{2}from the point a, below & at an angle of 30°, which is represented by the letter Φ, with the x-y line.

* Step-5* From the end points of these previously drawn lines (i.e. b’

_{1}& b

_{2 }) draw horizontal lines which are parallel with the line x-y.

* Step-6* From the point b’

_{1}draw a vertical line up to the x-y line in downward direction and perpendicular to the line x-y. Now make an arc with the point a’ as center and radius equal to the distance of the point of intersection of the previously drawn vertical line with the x-y line, which will cut the horizontal line passing through the point b

_{2}. And give the name of that point b.

* Step-7* Now draw a line between the points a & b, which is the plan of the line AB. Find its inclination with the x-y line, which is represented by the letter β.

* Step-8* From the point b

_{2 }draw a vertical line up to the x-y line in upward direction and perpendicular to the line x-y. Now make an arc with the point a as center and radius equal to the distance of the point of intersection of the previously drawn vertical line with the x-y line, which will cut the horizontal line passing through the point b’

_{1}. And give the name of that point b’.

* Step-9* Now draw a line between the points a’ & b’, which is the elevation of the line AB. Find its inclination with the x-y line, which is represented by the letter α.

* Step-10* Give the dimensions by any one method of dimensions and give the notations as shown into the figure. And make a list of the True Length & Angles made by the line AB as shown into the figure.