The diagonal of a rectangle is 284 millimeters, while the longer side is 234 millimeters. Find the shorter side of the rectangle and the angles the diagonal makes with each side rounded to the nearest whole number. **Problem Description:**The diagonal of a rectangle is 284 millimeters, while the longer side is 234 millimeters. Find the shorter side of the rectangle and the angles the diagonal makes with each side, rounded to the nearest whole number.**Instructions:**- **Shorter side:** Enter the length of the shorter side in millimeters (mm).- **Angle formed from short side and diagonal:** Enter the angle in degrees (°) formed between the shorter side and the diagonal.- **Angle formed from long side and diagonal:** Enter the angle in degrees (°) formed between the longer side and the diagonal.**Input Fields:**- Shorter side: __________ mm- Angle formed from short side and diagonal: __________ °- Angle formed from long side and diagonal: __________ °**Get Help:**- [eBook](#)---**Explanation:**1. **Determine the Shorter Side:** - Use the Pythagorean theorem to calculate the shorter side (a). Given diagonal (d) and longer side (b), the formula is: \[ d^2 = a^2 + b^2 \] Solving for \( a \): \[ a = \sqrt{d^2 - b^2} = \sqrt{284^2 - 234^2} \]2. **Find Angles Using Sine and Cosine Rules:** - To find the angles, utilize trigonometric relationships: \[ \theta_1 = \arcsin\left(\frac{\text{shorter side}}{\text{diagonal}}\right) \] \[ \theta_2 = \arccos\left(\frac{\text{longer side}}{\text{diagonal}}\right) \]Ensure to round your final answers to the nearest whole number.

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The diagonal of a rectangle is 284 millimeters, while the longer side is 234 millimeters. Find the shorter side of the rectangle and the angles the diagonal makes with each side rounded to the nearest whole number. shorter side: mm O angle formed from short side and diagonal: angle formed from long side and diagonal: O

The diagonal of a rectangle is 284 millimeters, while the longer side is 234 millimeters. Find the shorter side of the rectangle and the angles the diagonal makes with each side rounded to the nearest whole number. shorter side: mm O angle formed from short side and diagonal: angle formed from long side and diagonal: O

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter62: Volumes Of Prisms And Cylinders

Section: Chapter Questions

Problem 38A: A copper casting is in the shape of a prism with an equilateral triangle base. The length of each...

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