Damar is buying a new windsail for his sailboat. The triangular sail is attached between a vertical pole that creates a \( 90^{\circ} \) angle to the boat a horizontal pole that is attached at the bottom of the vertical pole. If th vertical pole is 22 feet tall and the horizontal pole is 8 feet, what is the angle of the sail that is formed at the top of the vertical pole? Round yo answer to the nearest whole degree. (1 point) The angle is approximately \( 70 \times \) Check answer Remaining Attempts :2

1. Draw the right triangle where the vertical pole is one leg (\(22\) ft), the horizontal pole is the other leg (\(8\) ft), and the sail is the hypotenuse. 2. The right angle is at the bottom of the vertical pole where the poles meet. Let the top of the vertical pole be point \(A\), the bottom (where the horizontal pole attaches) be point \(B\), and the end of the horizontal pole be point \(C\). 3. In triangle \(ABC\), side \(AB = 22\) ft and side \(BC = 8\) ft. The sail forms side \(AC\) (the hypotenuse) and is attached at point \(A\). 4. The angle between the sail and the vertical pole at point \(A\) is given by \[ \sin A = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{BC}{AC}. \] First, calculate \(AC\) using the Pythagorean theorem: \[ AC = \sqrt{AB^2 + BC^2} = \sqrt{22^2 + 8^2} = \sqrt{484 + 64} = \sqrt{548} = 2\sqrt{137}. \] 5. Thus, \[ \sin A = \frac{8}{2\sqrt{137}} = \frac{4}{\sqrt{137}}. \] 6. Evaluating the sine value: \[ \sqrt{137} \approx 11.70, \quad \frac{4}{11.70} \approx 0.341. \] Then, \[ A \approx \sin^{-1}(0.341) \approx 20^\circ. \] 7. The vertical pole makes a \(90^\circ\) angle with the boat. Therefore, the angle that the sail makes with the boat (at the top of the vertical pole) is the complement of \(A\): \[ 90^\circ - 20^\circ = 70^\circ. \] 8. Rounding to the nearest whole degree, the angle is approximately \[ 70^\circ. \]