Let's solve the problem step by step: --- ## **Problem Restatement** **Given:** - \( x = 4.4 \) m - \( y = 8.4 \) m - \( \alpha = 63^\circ \) **To Find:** The length of bar \( OA \). --- ## **Step 1: Understanding the Geometry** From the diagram, point \( O \) is at the origin, and \( A \) is at coordinates (x, y, z). The bar \( OA \) makes an angle \(\alpha\) with the x-y plane. --- ## **Step 2: Express the Length of OA** The length of OA is the distance from \( O \) to \( A \): \[ OA = \sqrt{x^2 + y^2 + z^2} \] We know \( x \) and \( y \), but need to find \( z \). --- ## **Step 3: Find \( z \) Using the Angle** The projection of OA onto the x-y plane is: \[ OA_{xy} = \sqrt{x^2 + y^2} \] The bar OA makes an angle \(\alpha\) with the x-y plane, so: \[ \sin\alpha = \frac{z}{OA} \] \[ z = OA \cdot \sin\alpha \] And: \[ \cos\alpha = \frac{OA_{xy}}{OA} \] \[ OA_{xy} = OA \cdot \cos\alpha \] \[ OA = \frac{OA_{xy}}{\cos\alpha} \] --- ## **Step 4: Calculate the Values** ### **Calculate \( OA_{xy} \):** \[ OA_{xy} = \sqrt{(4.4)^2 + (8.4)^2} = \sqrt{19.36 + 70.56} = \sqrt{89.92} = 9.49 \text{ m} \] ### **Calculate \( OA \):** \[ OA = \frac{9.49}{\cos 63^\circ} \] \[ \cos 63^\circ \approx .454 \] \[ OA = \frac{9.49}{.454} \approx 20.91 \text{ m} \] --- ## **Step 5: Round the Answer** Express your answer to two digits after the decimal point: \[ \boxed{20.91 \text{ m}} \] --- ## **Conclusion** **The length of the bar OA is \( \mathbf{20.91\ m} \) (rounded to two decimal places).**