This question requires us to use the cosine rule:
a^2 = b^2 + c^2 - 2bc*cos(A),
where A is the included angle between sides b and c, and a is the side of the triangle opposite to the angle.
In the context of the question, a is the length of the tunnel (let's call this t), b is 6 km, c is 7 km and A is 29°.
Given the values in the question and those we defined, we can rewrite the equation for the cosine rule as:
t^2 = 6^2 + 7^2 - 2(6)(7)cos(29)
Now, evaluating this we get:
t^2 = 36 + 49 - 84cos(29)
t^2 = 85 - 84cos(29)
t = sq.root (85 - 84cos(29))
= 3.40 km (rounded to two decimal places)
