Question

chance the pilot of a boeing 727 flew e plane so it took off at an angle of elevation 21 degrees. after flying one kilometer, what is the altitude (height) of the plane that chance was flying rounded to the nearest meter? (1 km= 1000 meters)

Answer 1

To solve the exercise, it is convenient to first draw a picture of the situation posed by the statement:

As you can see, a right triangle is formed. So to find the height at which the plane was when the pilot had flown one kilometer, you can use the trigonometric ratio sin(θ):

`\sin (\theta)=\frac{\text{Opposite side}}{\text{ Hypotenuse}}`

Then, in this case, you have

`\begin{gathered} \sin (21\text{\degree})=\frac{\text{ Altitude}}{1000m} \\ \text{ Multiply by 1000m on both sides of the equation} \\ \sin (21\text{\degree})\cdot1000m=\frac{\text{ Altitude}}{1000m}\cdot1000m \\ \sin (21\text{\degree})\cdot1000m=\text{ Altitude} \\ 358.37m=\text{ Altitude} \\ \text{ Rounding to the nearest meter} \\ 358m=\text{ Altitude} \end{gathered}`

Therefore, the altitude or height of the plane after flying one kilometer is 358 meters.