# Math Help - Angles of Elevation and Depression??

1. ## Angles of Elevation and Depression??

Suppose you live about 5.1 miles away from a tower. From your home, you see a plane directly above the tower. Your angle of elevation from the plane is 21º. What is the plane's altitude???

I don't understand how to solve this problem, so if someone could please help me that would be great!!

Thanks.

2. Hello, amberkraidich!

Suppose you live about 5.1 miles away from a tower.
From your home, you see a plane directly above the tower.
Your angle of elevation from the plane is 21º.
What is the plane's altitude?
If you make a sketch, a trig relation should suggest itself.
Code:
    P *
|   *
|       *
a |           *
|                *
|              21°  *
T * - - - - - - - - - - - * H
5.1

Your house is at $H$; the tower is at $T.\quad HT = 5.1\text{ miles}$

The plane is at $P.\quad PT = a\text{ miles}$

Relative to $\angle H = 21^o$, we have: . $opp\:=\:a,\;\;adj \:=\: 5.1$

What trig function is suggested?

3. Originally Posted by amberkraidich
Suppose you live about 5.1 miles away from a tower. From your home, you see a plane directly above the tower. Your angle of elevation from the plane is 21º. What is the plane's altitude???

I don't understand how to solve this problem, so if someone could please help me that would be great!!

Thanks.
Edit: Soroban, look at those post times....mere milliseconds apart!

Hi amber,

I think you meant to say that the angle of depression from the plane is 21 degees or that the angle of elevation from you to the plane is 21 degrees. Look at the diagram.

You will be wanting to solve for the plane's altitude (a).

Use the tangent function of 21 degrees with the ratio of the opposite side over the adjacent side of the angle.

$\tan 21 = \frac{a}{5.1}$

Answer will be in miles.

You might want to change 5.1 miles to feet to get a more appropriate answer.

$1 \ \ mi \ \ =5280$ feet.

$5.1 \ \ mi \ \ = 26928$ feet.

$\tan 21=\frac{a}{26928}$

Answer will be in feet.