Trigonometry Word Problem ...

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Jun 12th 2009, 12:16 PM
shadow6

Trigonometry Word Problem ...

The following questions are for a final class project. Obviously these questions are very hard, and I am unsure how to completely answer these with the proper and complete work shown. Help on answering these questions with work/ steps would be greatly appreciated.

3. A plane takes off in a straight line and travels along for 10 seconds were it reaches a height of 400m.
a) If the plane is traveling at a speed of 65m/s what distance does it travel?
b) At what angle is the plane ascending? Draw a diagram.
Jun 12th 2009, 12:37 PM
craig

Quote:

Originally Posted by shadow6

3. A plane takes off in a straight line and travels along for 10 seconds were it reaches a height of 400m.
a) If the plane is traveling at a speed of 65m/s what distance does it travel?

If it travels 65 metres in 1 second, then in 10 seconds it travels $65 \times 10$ metres.

Quote:

Originally Posted by shadow6

b) At what angle is the plane ascending? Draw a diagram.

If we draw a right angled triangle, the opposite side will be 400 metres, and the hypotenuse is what you have worked out above. If you have the opposite side and hypotenuse, what trigonometrical ratio can you use?

If you show us some working for these questions then we can help you where you go wrong.
Jun 12th 2009, 12:45 PM
shadow6

I remember doing this question and I recall getting the answer of 38 °. However when I got the 650m, I wasn't sure whether to put the 650 on the hypotenouse or the adjacent. I used the hypotenuse and remember solving the question using Cos. Would this be correct?

I don't have the sheet with me right now. We are only supposed to do it in class but I managed to copy down these questions on paper to try and work this out at home. I attempt many answers though I am not sure if I did certain steps the right way.
Jun 12th 2009, 12:49 PM
craig

Quote:

Originally Posted by shadow6

I remember doing this question and I recall getting the answer of 38 [FONT=&quot]°. However when I got the 650m, I wasn't sure whether to put the 650 on the hypotenouse or the adjacent. I used the hypotenuse and remember solving the question using Cos. Would this be correct?

I don't have the sheet with me right now. We are only supposed to do it in class but I managed to copy down these questions on paper to try and work this out at home. I attempt many answers though I am not sure if I did certain steps the right way.

The 650 would be the hypotenuse, it's the actual distance the plane has travelled.

I'm afraid you wouldn't use the Cos ratio, the correct one would be $\sin{\theta} = \frac{o}{h}$ , putting your values into this what do you get?
Jun 12th 2009, 12:51 PM
craig

A good way to remember the trig ratios is the word SohCahToa, (Sok-a-toe-a).

$\sin{\theta} = \frac{o}{h}$ , $\cos{\theta} = \frac{a}{h}$ , $\tan{\theta} = \frac{o}{a}$ .

Hope this helps
Jun 12th 2009, 12:58 PM
shadow6

My mistake, I meant 400 was the opposite height. The result was 38. :) Thanks very much for the help and clarification. Unfortunately that was one of the easy ones. :( The ones really confusing me are the ones involving the directions.

Sin A = 400 / 650
Sin A = 0.6154
A = Sin-1(0.6154)
A = 38°
Jun 12th 2009, 01:00 PM
craig

Quote:

Originally Posted by shadow6

Sin A = 400 / 650
Sin A = 0.6154
A = Sin-1(0.6154)
A = 38°

Correct!