Exercise 1: Solving a New Triangulation Problem With the Law of Sines — Possible Solution
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FINDING THE THIRD ANGLE
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Baseline AB = 200m, angle at A = 50 degrees, angle at B = 65 degrees.
The third angle, at the landmark (call it T), is found the same way
this chapter's own worked example found it:

    angle T = 180 - 50 - 65 = 65 degrees

COMPUTING THE TWO DISTANCES
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Using the Law of Sines exactly as this chapter's own worked example
did, AT/sin(B) = AB/sin(T) = BT/sin(A):

    AT = AB * sin(B) / sin(T) = 200 * sin(65) / sin(65) = 200.0m
    BT = AB * sin(A) / sin(T) = 200 * sin(50) / sin(65) = 169.05m

(computed precisely: AT = 199.99999999999997, matching 200 to
floating-point precision; BT = 169.04730469627978)

WHY AT CAME OUT EQUAL TO THE BASELINE ITSELF
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This isn't a coincidence or an error - it happens because angle B
(65 degrees) and angle T (65 degrees) are equal. Whenever two angles
of a triangle are equal, the sides opposite them are also equal (the
triangle is isosceles) - here, the side opposite angle B is AT, and
the side opposite angle T is AB. Since angle B = angle T, AT must
equal AB, which is exactly what the Law of Sines calculation
confirmed (up to a tiny floating-point rounding difference in the
last digit). This is a good, self-checking property: getting a result
that matches a known geometric fact (equal angles imply equal
opposite sides) here is a useful independent confirmation that the
calculation was set up correctly.

WHY THIS WORKS AS AN ANSWER
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The answer applies the Law of Sines correctly to compute both
distances, and additionally notices and explains the geometric reason
AT came out equal to the baseline itself (the isosceles-triangle
property from the coincidentally equal angles), which serves as a
built-in sanity check on the arithmetic rather than treating the
matching values as an unremarked coincidence.