Question

a plane is descending at an angle of 2° from the horizontal. the planes current altitude is 8.2 km. see the figure below. (the figure is not drawn to scale.) find the planes new altitude, h, after 0.20 hours if it travels at a constant speed of 500 km/hr along the direction of its flight. carry your intermediate computations to at least four decimal places, and round your answer to the nearest tenth of a kilometer.
h=□ kilometers

Explanation:

Step1: Calculate the distance the plane travels

The formula for distance \(d\) is \(d = v\times t\), where \(v = 500\) km/hr and \(t=0.20\) hours.
\(d=500\times0.20 = 100\) km.

Step2: Use the sine function to find the change in altitude

Let \(\theta = 2^{\circ}\). The change in altitude \(\Delta h\) is given by \(\sin\theta=\frac{\Delta h}{d}\). So \(\Delta h=d\times\sin\theta\).
Substitute \(d = 100\) km and \(\theta = 2^{\circ}\) (since \(\sin(2^{\circ})\approx0.0349\)):
\(\Delta h=100\times\sin(2^{\circ})\approx100\times0.0349 = 3.49\) km.

Step3: Calculate the new altitude \(h\)

The new altitude \(h\) is \(h = 8.2-\Delta h\).
\(h=8.2 - 3.49=4.71\approx4.7\) km.

Answer:

\(4.7\) kilometers