# 5.1 Phy1020: brief trigonometry tutorial  (Page 7/20)

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Then Listing 2 calls the toDegrees method, passing the value of angRad as a parameter and stores the returned value in a variable named angDeg .

Finally, Listing 2 calls the document.write method twice in success to display the angle values shown in Figure 5 .

Another exercise with a different viewpoint

Now let's approach things from a different viewpoint. Assume that

• You know the value of the angle in degrees.
• You know the length of the hypotenuse.
• You need to find the length of the opposite side.

Assume also that for some reason you can't simply measure the length of the opposite side. Therefore, you must calculate it. This is a common situation inphysics, so let's see if we can write a script that will perform that calculation for us.

Please create an html file containing the code shown in Listing 3 and open the file in your browser.

Listing 3 . Finding length of the opposite side.
```<!-- File JavaScript03.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 hyp = 5 var angDeg = 53.13var angRad = toRadians(angDeg) var sine = Math.sin(angRad)var opp = hyp * sine document.write("opposite = " + opp + "</br>") hyp = opp/sinedocument.write("hypotenuse = " + hyp + "</br>")</script></body></html>```

The output for the opposite side

When you open your html file in your browser, the output shown in Figure 3 should appear in your browser window.

Figure 6 . Output for script in Listing 3.
```opposite = 3.999994640742543 hypotenuse = 5```

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:

5*sin(53.1301024 degrees)

The following will appear immediately below the search box:

5 * sin(53.1301024 degrees) = 4

This is the length of the opposite side for the given angle and the given length of the hypotenuse.

Interesting equations

We learned earlier that the sine of the angle is equal to the ratio of the opposite side and the hypotenuse. We also learned that the angle is thearcsine of that ratio.

If we know any two of those values ( angle , opp , hyp ), we can find the third (with a little algebraic manipulation) as shown in Figure 7 .

Figure 7 . Interesting sine equations.
```sine(angle) = opp/hyp angle = arcsine(opp/hyp)opp = hyp * sine(angle) hyp = opp/sine(angle)```

Getting back to Listing 3

After defining the radian/degree conversion functions, Listing 3 declares and initializes variables representing the length of the hypotenuse and theangle in degrees. (Note that the angle in degrees was truncated to four significant digits, which may introduce a slight inaccuracy into thecomputations.)

Get and use the sine of the angle

That angle is converted to radians and passed as a parameter to the Math.sin method, which returns the value of the sine of the angle.

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