ANS:C - 1°43' 28"

The maximum deflection angle of a transition curve is given by the formula:

δ = L^2/6RL.

where:

L is the length of the transition curve.
R is the radius of the circular curve.
l is the length of the tangent.

In this case, L = 90 m and R = 500 m, so the maximum deflection angle is:
δ = 90^2 / 6 * 500 * 90 = 1°43'08".

Therefore, the correct answer is 1°43'08". CORRECT ANSWER IS A - 1°43"08' -Cofirmed from textbook

Explanation:

Max Deflection angle = L^2/6RL (this is in radians),
So in degrees, it will be =L ^2/6RL [180/π],
In minutes it will be = 1800 [L^2/RL].
Thus applying this formula we get max Deflection angle = 1°43"08'.

(For those asking where the 573 in the above explanations came from its simply 180/π =573). CORRECT ANSWER IS A - 1°43"08' -Cofirmed from textbook

Explanation:

Max Deflection angle = L^2/6RL (this is in radians),
So in degrees, it will be =L ^2/6RL [180/π],
In minutes it will be = 1800 [L^2/RL].
Thus applying this formula we get max Deflection angle = 1°43"08'.

(For those asking where the 573 in the above explanations came from its simply 180/π =573). L2/6RL.
500^2/(6*500*90)*(180).
=1'43'7.14".