Nagrom the dwarf queen desires a tunnel through the mountain to connect her two wealthiest cities, yram and haras, which lie on either side. in an effort to determine the length of the tunnel, nagrom first walks 7 km from yram to a point where she can see both cities. from that point, she measures 29, degree between the cities. lastly, she walks 6 km to haras. what is the length of the tunnel? do not round during your calculations. round your final answer to the nearest hundredth of a kilometer.

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)

3.40

Step-by-step explanation:

I checked the answer and it was right!!

126.66 m²

step-by-step explanation:

the pertinent area formula is a = πr², where r is the radius.

here, a = π(6.35 m)² = 40.32π, or approximately 126.66 m²