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The problem asks to determine the resultant force of two forces acting on an airplane wing: **Lift** (850 lb upward) and **Drag** (320 lb horizontally to the right). We need to find the magnitude of the resultant force and the angle it makes with the horizontal.

### Steps:

1. **Calculate the resultant force magnitude**:
   The resultant force \(\mathbf{R}\) can be found using the Pythagorean theorem:
   \[
   R = \sqrt{(\text{Lift})^2 + (\text{Drag})^2}
   \]
   Substituting the given values:
   \[
   R = \sqrt{(850)^2 + (320)^2}
   \]

2. **Find the angle**:
   The angle \(\theta\) between the resultant force and the horizontal can be calculated using the tangent function:
   \[
   \theta = \tan^{-1} \left( \frac{\text{Lift}}{\text{Drag}} \right)
   \]
   Substituting the given values:
   \[
   \theta = \tan^{-1} \left( \frac{850}{320} \right)
   \]

Let me compute these values for you.The magnitude of the resultant force is approximately **908 lb**, and the angle it makes with the horizontal is about **69.37°**.

Would you like more details on how these were calculated, or have any questions? 

Here are some related questions to explore:

1. How do we resolve forces in two dimensions?
2. Why is the Pythagorean theorem used for resultant force calculations?
3. How do you convert between radians and degrees in trigonometry?
4. How can we calculate force components if given an angle and a resultant force?
5. What are the real-world implications of lift and drag in aviation?

**Tip**: Always use the inverse trigonometric functions (like \(\tan^{-1}\)) to find angles when given opposite and adjacent sides.

Two forces that act on an airplane wing are called the lift and the drag. Find the resultant of these forces acting on the airplane wing.

Learn how to calculate the resultant force acting on an airplane wing using vector addition of lift and drag forces. This problem involves applying the Pythagorean theorem and trigonometric functions to determine the resultant force's magnitude and direction. Suitable for high school students in Grades 9-12.

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