# Thread: Trigonometry Help..... Totally stuck...

1. ## Trigonometry Help..... Totally stuck...

Hello, how are you?? I am totally confused on 2 problems and it has been causing me heartache. Could someone help me with it?

The first problem is:
A hot air balloon is floating above a straight road. To estimate their height above the ground, the balloonists simultaneously measure the angle of the depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 20 degrees and 22 degrees. How high is the balloon????

and the other one is:

To estimate the height of a mountain above a level plain, the angle of elevation to the top of the mountain is measured to be 32 degrees. One thousand feel closer to the mountain along the plain, it is found that the angle of elevation is 35 degrees. Estimate the height of the mountain.

Thanks for the help!

2. Originally Posted by Godzilla
Hello, how are you?? I am totally confused on 2 problems and it has been causing me heartache. Could someone help me with it?

The first problem is:
A hot air balloon is floating above a straight road. To estimate their height above the ground, the balloonists simultaneously measure the angle of the depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 20 degrees and 22 degrees. How high is the balloon????

and the other one is:

To estimate the height of a mountain above a level plain, the angle of elevation to the top of the mountain is measured to be 32 degrees. One thousand feel closer to the mountain along the plain, it is found that the angle of elevation is 35 degrees. Estimate the height of the mountain.

Thanks for the help!
let $x$ = horizontal distance from the closer milepost to a point directly below the balloon

$h$ = balloon height above the ground in miles

... consecutive mileposts are a mile apart.

$\tan(20) = \frac{h}{x+1}$

$h = (x+1)\tan(20)$

$\tan(22) = \frac{h}{x}$

$h = x\tan(22)$

$h = h$

$x\tan(22) = (x+1)\tan(20)$

$x\tan(22) = x\tan(20) + \tan(20)$

$x\tan(22) - x\tan(20) = \tan(20)$

$x[\tan(22)-\tan(20)] = \tan(20)$

$x = \frac{\tan(20)}{\tan(22)-\tan(20)}$

$h = \frac{\tan(20) \cdot \tan(22)}{\tan(22)-\tan(20)}$

second problem has the same solving strategy

3. Godzilla!

To estimate the height of a mountain above a level plain,
the angle of elevation to the top of the mountain is measured to be 32°.
One thousand feel closer to the mountain, the angle of elevation is 35^#176;.
Estimate the height of the mountain.
Code:
    A *
| * *
|   *   *
h |     *     *
|       *       *
|     35° *     32° *
*-----------*-----------*
B - - x - - C  - 1000 - D

The height of the mountain is: $H = AB$
$\angle ADB = 32^o,\;\angle ACB = 35^o$
$CD = 1000$
Let $x = BC$

Now follow the steps outlined by skeeter . . .