A tree on one side of a river is due west of a rock on the other side of the river. From a stake  yards north of the rock, the bearing of the tree is S 21.1 W. How far is it from the rock to the tree? Round to at least the nearest tenth of a yard.

To solve this problem, we can use trigonometry, specifically the tangent function, since we have an angle and a length of one side of the right triangle.

### Problem Setup:
1. Let the tree be point \( T \) and the rock be point \( R \). 
2. A stake is placed some distance north of the rock; let's call this point \( S \).
3. The bearing from the stake to the tree is S 21.1° W.

Since "S 21.1° W" means an angle of 21.1° measured counterclockwise from the south line towards the west, we can visualize a right triangle where:
- Point \( S \) is directly north of \( R \).
- The angle between the south line and the line \( ST \) is 21.1°.

Let's denote the distance between the rock \( R \) and the tree \( T \) as \( x \), and the distance between the stake \( S \) and the rock \( R \) as \( d \).

### Step-by-step Solution:

1. Draw a right triangle with:
   - The leg \( SR = d \) (distance north-south).
   - The leg \( RT = x \) (distance we need to find, east-west).
   - The angle at \( S \) is 21.1°.

2. The tangent of the angle can be defined as:
   
   \[
   \tan(21.1^\circ) = \frac{x}{d}
   \]

3. Solving for \( x \):

   \[
   x = d \times \tan(21.1^\circ)
   \]

4. Substitute the value of \( \tan(21.1^\circ) \):

   \[
   x = d \times \tan(21.1^\circ)
   \]

Now, let's calculate \( x \) using \( \tan(21.1^\circ) \). I'll perform the calculation. Please provide the value of \( d \) if it’s available. If not, I'll show you the calculations assuming \( d = 1 \) yard, and you can adjust the value accordingly.

A tree on one side of a river is due west of a rock on the other side of the river. From a stake yards north of the rock, the bearing of the tree is S 21.1° W. How far is it from the rock to the tree? Round to at least the nearest tenth of a yard.

Learn how to calculate the distance between a tree and a rock across a river using trigonometric functions. This problem involves angles, bearings, and right triangles, suitable for students in Grades 9-12. Solve for the distance using the tangent function and bearing angle of S 21.1° W.

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