Expert: Paul Klarreich - 12/3/2007

Question
QUESTION: Hi I was asked to find an angle. i guess that is what she meant it was a 0 with a line through the 0,than round to the nearest degree
here it is  a right triangle with a base of 6ft and side of 4ft the hypotense side blank the angle sign is in the right hand corner inside of the triangle, i don't know where to begin? i am told it is basic but it is new to me.

ANSWER: Questioner:   sue
Category:  Advanced Math
Private:  No
 
Subject:  Trig angles
Question:  Hi I was asked to find an angle. i guess that is what she meant it was a 0 with a line through the 0,than round to the nearest degree
here it is  a right triangle with a base of 6ft and side of 4ft the hypotense side blank the angle sign is in the right hand corner inside of the triangle, i don't know where to begin? i am told it is basic but it is new to me.
.................................
Hi, Sue,

These are all basic, AFTER YOU DO THEM.  Before that, they are impossible. But on to the example.
=======================================================
WARNING: USE COURIER FONT TO VIEW THIS
===================================================


I think your picture looks like this: (not completely to scale, and flipped, but it's the best I can do.)


     /|
    / |
   /  |
Hyp/   | 4 = leg opposite @ [theta, the name of the angle, and that
 /    |          funny thing you were describing.]  
/@    |
------+
6 = leg adjacent to @

In the future be sure to use this vocabulary -- being careless or vague about the words is a guaranteed way to lose the meaning of what you are doing.

NOW, then, there are six TRIGONOMETRIC FUNCTIONS DEFINED ON THIS TRIANGLE:
(and you will be expected to memorize them, using this vocabulary.)

       leg opposite @
sin @ = -----------
       hypotenuse

       leg adjacent to @
cos @ = --------------
       hypotenuse       

       leg opposite @
tan @ = -----------------
       leg adjacent to @
(that's enough for now)

In this case, you need the third one, since you don't have the hypotenuse (yet).
         4
tan @ = -----
         6

Now you can do the arithmetic.  Take out your (Windows) calculator, put it in SCientific view, and do this:

Enter 4
Press /
Enter 6
Press =
Click Inv
Press tan

You get 33.69006752597978691352549456166, which rounds to 34 degrees.


---------- FOLLOW-UP ----------

QUESTION: Question whuch is a reading problem
A search light is 520feet from a building. The beam lights up the building at a point 150 feet above the ground. What angle does the beam make from the ground? This is exact wording

Answer
Questioner:   sue
Category:  Advanced Math
Private:  No
 
Subject:  Trig angles


---------- FOLLOW-UP ----------

QUESTION: Question whuch is a reading problem
A search light is 520feet from a building. The beam lights up the building at a point 150 feet above the ground. What angle does the beam make from the ground? This is exact wording
----------------------------------------------------
Hi, Sue,

I think your diagram looks like this:

         /|
         /    |
         /       |
        /          | 150
     /          |
|  / t          |
-O -----------------+
|       520

t = theta, the angle the beam makes from the ground. (a.k.a. angle of elevation)


Recall these definitions, (which you memorized, right?)


       leg opposite t
sin t = -----------
       hypotenuse

       leg adjacent to t
cos t = --------------
       hypotenuse       

       leg opposite t
tan t = -----------------
       leg adjacent to t


Since 150 is the leg opposite t and 500 is the leg adjacent to t, you will know to use the definition for tan t, and do this with your calculator:

Enter 150
Press   /
Enter 500
Press   =
Check Inv
Click Tan

You get t = 16.699244233993621840368847179984, or 17 degrees.