A rope from the top of a mast on a sailboat is attached to a point 19 feet from the mast. If the rope is 28 feet long. how tall is the mast? Round to the nearest tenth of a foot.

To determine the height of the mast, we can use the Pythagorean theorem. Here's a step-by-step breakdown: 1. **Identify the Right Triangle Components:** - **Horizontal distance from the mast (base):** 19 feet - **Length of the rope (hypotenuse):** 28 feet - **Height of the mast (vertical side):** \( h \) feet 2. **Apply the Pythagorean Theorem:** \[ h^2 + 19^2 = 28^2 \] 3. **Calculate the Squares:** \[ h^2 + 361 = 784 \] 4. **Solve for \( h^2 \):** \[ h^2 = 784 - 361 = 423 \] 5. **Find \( h \):** \[ h = \sqrt{423} \approx 20.566 \text{ feet} \] 6. **Round to the Nearest Tenth:** \[ h \approx 20.6 \text{ feet} \] **Therefore, the height of the mast is approximately 20.6 feet.**