1. The problem states that an airplane is 5,000 ft above the ground and must land on a runway 7,000 ft away horizontally. We need to find the correct trigonometric equation to calculate the angle $x$ the pilot takes to land. 2. The triangle formed is a right triangle with: - Opposite side to angle $x$: 5,000 ft (vertical height) - Adjacent side to angle $x$: 7,000 ft (runway distance) 3. Recall the definitions of sine and tangent for angle $x$ in a right triangle: - $\sin x = \frac{\text{opposite}}{\text{hypotenuse}}$ - $\tan x = \frac{\text{opposite}}{\text{adjacent}}$ 4. Since we know the opposite side (5,000 ft) and adjacent side (7,000 ft), but not the hypotenuse, the tangent function is appropriate here. 5. Therefore, the correct equation is: $$\tan x = \frac{5,000}{7,000}$$ 6. Simplifying the fraction: $$\tan x = \frac{5,000}{7,000} = \frac{5}{7}$$ 7. So the pilot's angle $x$ can be found by calculating $x = \tan^{-1}\left(\frac{5}{7}\right)$. Final answer: $\tan x = \frac{5,000}{7,000}$