An athlete participating in a paragliding competition was to reach the landing area B located 34 miles east of the starting position A. Due to the north wind, the athlete deviated from the intended course and landed directly south of B. The bearing from the starting position to the actual landing point is S 79.9° E. How far is the landing point from B? Round your answer to two decimal places.


We are given the following information about the athlete's paragliding path:

- The athlete starts at point \( A \), which is 34 miles directly west of the intended landing point \( B \).
- The athlete deviates due to wind and lands directly south of point \( B \), but the bearing from \( A \) to the landing point \( C \) is \( S 79.9^\circ E \).
- We need to determine how far the athlete is from the intended landing point \( B \) after deviating.

### Step 1: Visualize the scenario
We can represent this situation using a right triangle:
- Point \( A \) is at the starting position.
- Point \( B \) is 34 miles directly east of \( A \).
- The bearing from \( A \) to \( C \) forms an angle of \( 79.9^\circ \) south of east.

### Step 2: Set up the triangle
- The horizontal leg of the triangle is the distance from \( A \) to \( B \), which is 34 miles.
- The angle between the line \( AB \) (which is due east) and the line \( AC \) (the bearing from \( A \) to the landing point) is \( 79.9^\circ \).
- We need

An athlete participating in a paragliding competition was to reach the landing area B located 34 miles east of the starting position A. Due to the north wind, the athlete deviated from the intended course and landed directly south of B. The bearing from the starting position to the actual landing point is S 79.9° E. How far is the landing point from B? Round your answer to two decimal places.

Find how far an athlete lands from the intended point after deviating due to wind. This problem uses trigonometric concepts, the Law of Cosines, and bearings to solve for the distance. Suitable for Grades 9-12 students learning trigonometry.

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