# trigonometry word problem

• Oct 7th 2008, 03:03 PM
robasc
trigonometry word problem
When an airplane leaves the runway, its angle of climb is 20° and its speed is 335 feet per second. How long will it take the plane to climb to an altitude of 10,000 feet? 16,000 feet?

Here is how I am thinking about it:

335 * 60 = 20100

then 10,000 / 335 = 29.85 seconds.

I am not sure if this is right but it is a guess. Could some one help me.
• Oct 7th 2008, 03:06 PM
icemanfan
You need to use the vertical component of the plane's velocity, which is $\displaystyle 335 \sin 20$ feet per second, to calculate the time taken to reach a certain altitude.
• Oct 7th 2008, 03:08 PM
skeeter
vertical rate of climb is $\displaystyle 335\sin(20)$ ft/sec

now calculate time to climb ... $\displaystyle t = \frac{altitude}{rate \,\, of \,\, climb}$
• Oct 7th 2008, 03:14 PM
masters
Quote:

Originally Posted by robasc
When an airplane leaves the runway, its angle of climb is 20° and its speed is 335 feet per second. How long will it take the plane to climb to an altitude of 10,000 feet? 16,000 feet?

Here is how I am thinking about it:

335 * 60 = 20100

then 10,000 / 335 = 29.85 seconds.

I am not sure if this is right but it is a guess. Could some one help me.

I looked at it this way.

$\displaystyle \sin20=\frac{h}{335}$ should yield the height in feet after 1 second.

That's $\displaystyle 335 \sin 20$ ft. in 1 sec.

Now, for 10000 feet, that'd be $\displaystyle \frac{10000}{335 \sin 20} \approx 886 \ \ sec. \ \ or \ \ 14.8 \ \ min.$

Edit: Too slow on the post today!