Sure! Let's solve the problem step by step. Here's the question restated for clarity: --- **A trapeze artist swings on a 5.2 m long bar. If the support ropes make an angle of 33.° with the vertical, what is the vertical distance below the support bar?** --- ## **Step 1: Draw and Understand the Problem** The trapeze forms a triangle with: - Rope length = 5.2 m (hypotenuse) - Angle with vertical = 33.° We’re looking for the **vertical distance** from the support bar to the artist. This is the **adjacent side** of the triangle (cosine relation). **Explanation:** The vertical distance below the support bar is given by the adjacent side in the right triangle formed by the rope and the vertical. Use cosine, since: \[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \] --- ## **Step 2: Calculate the Vertical Distance** \[ \cos(33^\circ) = \frac{h}{5.2} \] \[ h = 5.2 \cdot \cos(33^\circ) \] \[ h = 5.2 \cdot .8387 \approx 4.36 \text{ m} \] **Explanation:** Multiplying the rope length by the cosine of the angle gives the vertical height from the support bar to the artist. --- ## **Final Answer** \[ \boxed{4.36\ \text{m}} \] This is the **vertical distance below the support bar**.