Question

25 a helicopter takes off and travels forward at an angle of 59.4° above horizontal. after following this path for 294 meters, the pilot changes the angle of flight to 10.5° above horizontal and follows this path for 849 meters. after these two legs, what is the helicopters horizontal distance from the point of take off? 408 m 447 m 964 m 985 m

Explanation:

Step1: Calculate the horizontal distance for the first leg

The horizontal distance \(x_1\) for the first leg is given by \(x_1 = d_1\cos\theta_1\), where \(d_1 = 294\) m and \(\theta_1=59.4^{\circ}\).

$$x_1=294\times\cos(59.4^{\circ})$$

Using a calculator, \(\cos(59.4^{\circ})\approx0.506\), so \(x_1 = 294\times0.506=148.764\) m.

Step2: Calculate the horizontal distance for the second leg

The horizontal distance \(x_2\) for the second leg is given by \(x_2 = d_2\cos\theta_2\), where \(d_2 = 849\) m and \(\theta_2 = 10.5^{\circ}\).

$$x_2=849\times\cos(10.5^{\circ})$$

Using a calculator, \(\cos(10.5^{\circ})\approx0.983\), so \(x_2=849\times0.983 = 834.567\) m.

Step3: Calculate the total horizontal distance

The total horizontal distance \(x=x_1 + x_2\).

$$x=148.764+834.567=983.331\approx985$$

m

Answer:

985 m