Expert: Paul Klarreich - 11/11/2008

Question
This is not my homework i want to get in this vey prestigous high school and it is required to know this stuff i understand the basis but thats about it PLEASE HELP!
The foot of a ladder is 1.5m from a vertical wall. The ladder makes an angle of 68 degrees with the horizontal. How far up the wall does the ladder reach

Answer
Questioner:   Breanna
Category:  Advanced Math
Private:  No
 
Subject:  triginometry ratios
Question:  This is not my homework i want to get in this vey prestigous high school and it is required to know this stuff i understand the basis but thats about it PLEASE HELP!
The foot of a ladder is 1.5m from a vertical wall. The ladder makes an angle of 68 degrees with the horizontal. How far up the wall does the ladder reach
..................................
Hi, Breanna,

I assume you mean Bronx High School of Science (there really is no other) and I wish you the best.  (You might pay some attention to your grammar and punctuation -- that will surely help.)

You have learned that in this right triangle, where t represents the acute angle theta:

    /|
   / |
hyp/  |
 /   |opp leg
/    |
/t    |
------+
adj leg

1. The terms adjacent leg and opposite leg mean adjacent to theta and opposite theta.

2. The basic trigOnometric ratios are defined:
       opposite leg
sin t = ------------
       hypotenuse

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

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

So to do this example, you match things:

    /|
   / |
hyp/  |
 /   |reaching
/    |up
/68d  |
------+
1.5 m

(Sorry, I can't make a degree symbol.)


68d matches t.
reaching up matches opposite leg.
1.5 m  matches adjacent leg.

Use:

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

and do the matching:

        reaching up
tan 68 = ------------
           1.5

Now you look up tan 68, and just cross-multiply.

With my calculator I get  3.7126302801244437378600198691143 meters.