Question

1. an airplane climbs at an angle of 18° with the ground. find the ground distance the plane travels as it moves 2500 m through the air.

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the hypotenuse (distance through the air) \(c = 2500\) m and the angle with the ground \(\theta=18^{\circ}\), and we want to find the adjacent side (ground distance) \(x\). Using the cosine function: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), so \(x = c\cos\theta\).

Step2: Substitute the values

Substitute \(c = 2500\) and \(\theta = 18^{\circ}\) into the formula. \(\cos(18^{\circ})\approx0.9511\). Then \(x=2500\times\cos(18^{\circ})\).

Step3: Calculate the value

\(x = 2500\times0.9511=2377.75\) m.

Answer:

The ground distance the plane travels is approximately \(2377.75\) m.