Question

an airplane is 5,000 ft above ground and has to land on a runway that is 7,000 ft away as shown above. let x be the angle the pilot takes to land the airplane at the beginning of the runway. which equation is a correct way to calculate x?

o sin x = 5,000/7,000

o sin x = 7,000/5,000

o tan x = 5,000/7,000

o tan x = 7,000/5,000

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle, the tangent of an angle is defined as the ratio of the opposite side to the adjacent side, and the sine of an angle is the ratio of the opposite side to the hypotenuse. Here, the height of the airplane above the ground (5000 ft) is the opposite side of the angle \(x\), and the horizontal distance to the runway (7000 ft) is the adjacent side of the angle \(x\).

Step2: Identify the correct trigonometric ratio

Since we have the opposite and adjacent sides with respect to the angle \(x\), we use the tangent function. The formula for the tangent of an angle \(x\) in a right - triangle is \(\tan x=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan x = \frac{5000}{7000}\).

Answer:

C. \(\tan x=\frac{5000}{7000}\)