Sue is in an airplane which travels at a constant 300 kilometers per hour. The angle of climb of the airplane is 30 ∘ . How long (in seconds) would it take from takeoff, before the airplane reaches 3000 meters, when Sue can access Wifi and work on the rest of the weekly problems?

Question

Sue is in an airplane which travels at a constant 300 kilometers per hour. The angle of climb of the airplane is 30 ∘  . How long (in seconds) would it take from takeoff, before the airplane reaches 3000 meters, when Sue can access Wifi and work on the rest of the weekly problems?

anonymous · Answer

The distance traveled is equal to the velocity times the time travelled. So, lets convert the airplane's speed to m/s:
$$300 km/h \times \frac{ .277777 m/s }{ 1 km/h } = 83.33333 m/s$$So, after t seconds, the plane will travel 83.33333t meters. Now lets make a picture using this distance:
|dw:1374861515709:dw| 
Do you know how to solve from here?

anonymous · Answer

Unfortunately i do not :( I just wanted to know the answer.

anonymous · Answer

DO you use a trig function

anonymous · Answer

Yes, you could use sine, since we have the side opposite the angle and the hypotenuse, or we can use the law of sines

anonymous · Answer

sin$$\sin30=3000/83.3333$$

anonymous · Answer

like that?

anonymous · Answer

Yes, but you left out the variable, which should go with the 83

anonymous · Answer

$$\sin 30 = 3000 / (83.33333t)$$

anonymous · Answer

$$t=3000/\sin30(83.333)$$

anonymous · Answer

Exactly, so what are you getting as an answer?

anonymous · Answer

i dont' have a calculator with me

anonymous · Answer

Ok, I'm getting 72 seconds

anonymous · Answer

that's correct