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 horizontal distance for first leg

Use the formula \(x = d\cos\theta\). For the first leg, \(d = 294\) m and \(\theta=59.4^{\circ}\). So \(x_1=294\cos(59.4^{\circ})\).
Using a calculator, \(\cos(59.4^{\circ})\approx0.506\), then \(x_1 = 294\times0.506=148.764\) m.

Step2: Calculate horizontal distance for second leg

For the second leg, \(d = 849\) m and \(\theta = 10.5^{\circ}\). Use the formula \(x = d\cos\theta\). So \(x_2=849\cos(10.5^{\circ})\).
Using a calculator, \(\cos(10.5^{\circ})\approx0.983\), then \(x_2=849\times0.983 = 834.567\) m.

Step3: Sum the two horizontal distances

\(x=x_1 + x_2\). Substitute \(x_1 = 148.764\) m and \(x_2=834.567\) m.
\(x=148.764+834.567 = 983.331\approx985\) m.

Answer:

985 m