# A fire is spotted 29 degrees west of South. The fire is 58 km from the look out station. A fire fighting base is 62 km due west of the first station. How far is the fire from the fighting base?

If the lookout is at the origin, the base is at

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Using trigonometry, we can find the distance from the fire to the fighting base. Since the fire is 29 degrees west of South, it forms a right triangle with the lookout station and the fighting base.

We can use the tangent function to find the distance from the fire to the fighting base.

Tangent of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Let's denote the distance from the fire to the fighting base as ( x ).

Thus, ( \tan(29^\circ) = \frac{58}{x} ).

Solving for ( x ), we get ( x = \frac{58}{\tan(29^\circ)} ).

Using a calculator, we find that ( \tan(29^\circ) \approx 0.5543 ).

So, ( x \approx \frac{58}{0.5543} ).

( x \approx 104.61 ) kilometers.

Therefore, the fire is approximately 104.61 kilometers from the fighting base.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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