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The code in Listing 2 uses the opposite side and the hypotenuse along with the arcsine to compute the angle. The code in Listing 6 uses the opposite side and the adjacent side along with the arctangent to compute the angle. Otherwise,no further explanation should be required.
Interesting tangent equations
In the spirit of Figure 5 and Figure 6 , Figure 9 provides some interesting equations that deal with the angle, the opposite side, and the adjacent side.Given any two, you can find the third using either the tangent or arctangent.
| Figure 9 . Interesting tangent equations. |
|---|
tangent(angle) = opp/adj
angle = arctangent(opp/adj)opp = tangent(angle) * adj
adj = opp/tangent(angle) |
An exercise involving the tangent
Please copy the code from Listing 7 into an html file and open it in your browser.
| Listing 7 . Finding the length of the opposite side. |
|---|
<!-- File JavaScript07.html --><html><body><script language="JavaScript1.3">function toRadians(degrees){
return degrees*Math.PI/180}//end function toRadians
//============================================//function toDegrees(radians){
return radians*180/Math.PI}//end function toDegrees
//============================================//var adj = 3
var angDeg = 53.13var angRad = toRadians(angDeg)
var tangent = Math.tan(angRad)var opp = adj * tangent
document.write("opposite = " + opp + "<br/>")
adj = opp/tangentdocument.write("adjacent = " + adj + "<br/>")</script></body></html> |
When you open your html file in your browser, the output shown in Figure 10 should appear in your browser window. We can see that the values in Figure 10 are correct for our 3-4-5 triangle.
| Figure 10 . Output for script in Listing 7. |
|---|
opposite = 3.9999851132269173
adjacent = 3 |
Very similar code
The code in Listing 7 is very similar to the code in Listing 3 and Listing 5 . The essential differences are that
You should be able to work through those differences without further explanation from me.
The cotangent of an angle
There is also something called the cotangent of an angle, which is simply the ratio of the adjacent side to the opposite side. If you know how to work withthe tangent, you don't ordinarily need to use the cotangent, so I won't discuss it further.
Computing length of opposite side with the Google calculator
We could also compute the length of the opposite side using the Google calculator.
The length of the opposite side -- sample computation
Enter the following into the Google search box:
3*tan(53.1301024 degrees)
The following will appear immediately below the search box:
3 * tan(53.1301024 degrees) = 4.00000001
Up to this point, we have dealt exclusively with angles in the range of 0 to 90 degrees (the first quadrant). As long as you stay in the firstquadrant, things are relatively straightforward.
As you are probably aware, however, angles can range anywhere from 0 to 360 degrees (or more). Once you begin working with angles that are greater then 90 degrees,things become a little less straightforward.
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