A magnetic azimuth of $54^\circ30'$ was observed along line AD in June 1977. The declination for the area surveyed is found by interpolation from an isogonic chart dated 1970 to be $17^\circ30'E$ with an annual change of $1'$ westward. The problem asks us to compute the true azimuth of line AD.

1. Problem Description

A magnetic azimuth of $54^\circ30'$ was observed along line AD in June

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7. The declination for the area surveyed is found by interpolation from an isogonic chart dated 1970 to be $17^\circ30'E$ with an annual change of $1'$ westward. The problem asks us to compute the true azimuth of line AD.

2. Solution Steps

First, we need to calculate the change in declination from 1970 to

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7. The number of years between 1970 and 1977 is $1977 - 1970 = 7$ years.

The annual change is $1'$ westward.

So, the total change in declination is $7 \text{ years} \times 1'/ \text{year} = 7'$. Since the change is westward, it is $-7'$.

Next, we calculate the declination in

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7. Declination in 1970 is $17^\circ30'E$.

Change in declination is $-7'$.

Declination in 1977 = $17^\circ30' - 7' = 17^\circ23'$.

Now we can compute the true azimuth of line AD.

The magnetic azimuth is $54^\circ30'$.

The declination in 1977 is $17^\circ23'E$.

Since the declination is east, we add the declination to the magnetic azimuth to find the true azimuth.

True Azimuth = Magnetic Azimuth + Declination

True Azimuth = $54^\circ30' + 17^\circ23' = 71^\circ53'$.

3. Final Answer

The true azimuth of line AD is $71^\circ53'$.