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For example, we know that the tangent of the angle at the origin on your graph board is 1.333. From that, we can determine the value of the angle.
The arctangent of an angle -- sample computation
Enter the following into the Google search box:
arctan(4/3) in degrees
The following will appear immediately below the search box:
arctan(4/3) = 53.1301024 degrees
We can also write a JavaScript script to perform the calculation.
Getting the angle for a known tangent value using JavaScript
Please create an html file containing the code shown in Listing 6 and open it in your browser.
| Listing 6 . Arctan of 3-4-5 triangle. |
|---|
<!-- File JavaScript06.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 opp = 4
var adj = 3var ratio = opp/adj
var angRad = Math.atan(ratio)var angDeg = toDegrees(angRad)
document.write("radians = " + angRad + "</br>")
document.write("degrees = " + angDeg)</script></body></html> |
The output from the script
Once again, when you open this file in your browser, the output shown in Figure 5 should appear in your browser window.
The code in Listing 6 is very similar to the code in Listing 2 . They both describe the same right triangle, so the output should be thesame in both cases.
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 7 and Figure 8 , Figure 11 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 11 . 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 12 should appear in your browser window. We can see that the values in Figure 12 are correct for our 3-4-5 triangle.
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