AZAX,
Instead of simply giving you the solutions, I have provided two very similar questions and worked solutions below.
Please go through these and then try to answer your two questions.
SCALE 6.
On a direct Mercator projection, at latitude 45° North, a certain length represents 70 NM. At latitude 30° North, the same length represents approximately?
a. 86 nm.
b. 75 nm.
c. 45 nm.
d. 90 nm.
This type of problem can be solved using the standard equation:
Distance at A / Distance at B = Cos A / Cos B
This can be rearranged to give:
Distance at B = (Distance at A x Cos B) / Cos A
Where A and B are latitudes.
For this question use A = 45 N, and Distance at A = 70 nm
And B = 30 N, and distance at B is to be calculated
Inserting these values into the equation gives:
Distance at B = (70 nm x Cos 30) / Cos 45 = 85.73 nm or approximately 86 nm (option a).
CHART THEORY 8.
What is the constant of the cone for a Lambert's Conic projection whose standard parallels are at 50 degrees North and 70 degrees North?
a. 0.866.
b. 0.500.
c. 0.941.
d. 0.766.
The constant of the cone is equal to the sine of the parallel of origin.
The parallel of origin is midway between the two standard parallels.
So in this question
Parallel of origin = (50 + 70) / 2 = 60N
Constant of the cone = sine of 60 = 0.866 (option a).