Expert: Cynthia Watanabe - 5/14/2006

Question
I am having problems with telling questions like this: ( A ladder 14 feet long rests against the side of a building. The base of the ladder rests on level ground 2 feet from the side of the building. What angle does the ladder form with the ground?) apart. Like what should it be solved with, Sin Cos or Tan?

Answer
Ashley,

Trig. questions are best solved by drawing a picture. When you see it, then your brain can usually fiqure it out.

It's difficult to draw here but it would help if you drew a right triangle. The vertical line is the building; the horizontal line is the ground;and the slant line(the hypotenuse) is the ladder leaning against the building.

Now, label the vertices starting at the top and going clockwise, A,B,C.  That way, we can talk about the angles and sides better.

Also, label the sides with the measures given in  your problem.  The horizontal line is 2 ft.; the slant line is 14 ft.

Since you are looking for the angle that is formed by the ladder and the ground, you should think of yourself as standing at angle B.  

To determine which trig. function to use, you need to know the ratios for each.
Sin A = opposite side/hypotenuse;
Cos A = adjacent side/hypotenuse;
Tan A = opposite side/adjacent side.

Since you were given measures for the horizontal side and the slant side, you need to set these in a ratio.
If you are standing at angle B, then the horizontal side (BC) is adjacent to you. The slant line (AB) is always the hypotenuse b/c it is opposite the 90 degree angle.

The only trig. function that has a ratio of adjacent side/hypotenuse is Cos A.

So the equation that you need is Cos B = 2/14.  
Since you are solving for the angle, you will need to use the Inverse Cosine.  So cos (to the -1 power) is the symbol for inverse cosine.

Cos (to the -1 power)[of] 2/14 = Angle B.

Type this into your calculator to find the answer.

These types of problems take practice.
Here's a website or two which are interactive so you can check your answers.
http://www.algebralab.org/lessons/lesson.aspx?file=Trigonometry_TrigApplications...
or
http://enlvm.usu.edu/ma/nav/bb_school.jsp?sid=emready&coid=geometry
or
http://www.intmath.com/TrigFns/TrFn.php

Keep asking questions! Take care, Cynthia