1. ## Speed

An airplane flying at an altitude of 10,000 feet passes directly over a fixed object on the ground. One minute later, the angle of depression of the object is 42 degrees. Approximate the speed of the airplane to the nearest mile per hour.
Ans: 126 mi/hr

$a= 10000/tan 42 degrees = 4364.2$

Is this right so far? if so what do I do next, or what do I do to make it right?

2. Originally Posted by purplec16
An airplane flying at an altitude of 10,000 feet passes directly over a fixed object on the ground. One minute later, the angle of depression of the object is 42 degrees. Approximate the speed of the airplane to the nearest mile per hour.
Ans: 126 mi/hr

$a= 10000/tan 42 degrees = 4364.2$

Is this right so far? if so what do I do next, or what do I do to make it right?
You setup is okay but you need to change your calculator to degree mode from radian mode!

After that make sure to look at you units. You are asked for an answer in $\frac{miles}{hr}$

The units of your answer will be in $\frac{ft}{min}$ just make sure to convert.

3. So I changed my mode, thanks, but what am I supposed to do to calculate the answer did i use the right triogonometric function

4. Hello, purplec16!

An airplane flying at an altitude of 10,000 feet passes directly over a fixed object on the ground.
One minute later, the angle of depression of the object is 42°.
Approximate the speed of the airplane to the nearest mile per hour.
Ans: 126 mi/hr

$a\:=\: \frac{10,\!000}{\tan42^o}\:=\: 4364.2$ ??

Is this right so far? . . . . no
Code:
              a
* - - - - - *
|     42° *
|       *
10,000 |     *
|   *
| *
*
Your set-up is correct, but . . .

. . $a \:=\:\frac{10,\!000}{\tan42^o} \:=\:11,\!106.12515$

The plane flew: . $11,\!106.12515$ feet in one minute.

It would fly: . $60 \times 11,\!106.12515 \:=\:66,\!367.509$ feet in one hour.

It would fly: . $66,\!367.509 \div 5280 \:=\:126.2059676$ miles in one hour.

Therefore, its speed is about 126 mph.

5. Where'd you get 5280 from, why'd you use that?

6. Originally Posted by purplec16
Where'd you get 5280 from, why'd you use that?

$\left(\frac{11106ft}{min} \right)$

You need to convert to MPH

so we have two converstion factors

$1 \text{mile} = 5280 ft$ and $60 \text{min}= 1 \text{hr}$

Using these gives

$\left(\frac{11106ft}{min} \right)\left(\frac{1 mile}{5280 ft}\right)\left(\frac{60 min}{1hr} \right)=126$

7. Hi purplec16,

1 mile=5280 feet.

your initial error was that your calculator was set to radians instead of degrees.
There are 360 degrees in a circle, which is the same as $2{\pi}$ radians.

Then you find how many feet the plane travels in a minute from the diagram.

In 60 minutes, it will travel 60 times that distance.

That is the speed in feet per hour.

You need the speed in miles per hour.

So the conversion is 1 mile = 5280 feet.

Hence divide by 5280 for your final answer.

8. Thanks I got it I understand now I forgot about the conversions part I was wondering why my answer was so big it clicked to me when he said it, Thanks again The Empty Set and Archie.