Bearing of a line to Origin

[305Gurl]

Problem statemen:

A curve with a bearing of back tangent of N70dE has a deflection angle from back tangent to forward tangent of 35d right. What is the bearing of the line from the PI to the origin (O)?

I thought I did this problem correctly, but I was incorrect. The way how the solution is given made me a little confused. What are they calling the origin. Is it the starting point of the intersecting angle? The question didn't provide a diagram which makes the problem more confusing. They solved it as follow:

Find Theta (the unknown angle near the PI): Theta= 180d-90d-(I/2) ......I don't understand where this 90d is from

where I =35d (given)

then theta = 72.5d

They then say find the bearing of the line from PI to the origin "O"

Theta= 180d-72.5d-35d-70d

where theta = 2.5d = S2D30'00"E

could someone explain this a bit better to me.

 

[civilized_naah]

Problem statemen:

A curve with a bearing of back tangent of N70dE has a deflection angle from back tangent to forward tangent of 35d right. What is the bearing of the line from the PI to the origin (O)?

could someone explain this a bit better to me.

The origin, I assume, is the center of the curve (bad choice of words – confusing)

The back tangent has a bearing N70E, which means the azimuth is also 70deg

The (inward) radius from PC to center is 90 degrees clockwise from the back tangent, therefore has an azimuth of 70+90 = 160.

Therefore, the outward radius R1 (from center to PC) has an azimuth of 160+180 = 340

Since the outward radius R2 from center to PI is I/2 clockwise from R1, it has an azimuth of 340+17.5 = 357.5

Therefore, the (inward radius) from PI to center has an azimuth of 357.5-180 = 177.5

This, expressed as a bearing is S2.5E

If you have the All In One Second Edition, this is explained on page 725

 

[ptatohed]

This is what I got: Back tangent with N 70^ E with I = 35^ means 180^ - I = 180^ - 35^ = 145^. 1/2 of 145^ = 72.5^. Form the PI, siting the back tangent, turn the back tangent 72.5^ left (or east) to the center of curve, O. Resultant bearing = S 2^ 30' 00" E. Ugly sketch attached:

 

[305Gurl]

Thanks again. Appreciated!