0.13 Phy1100: force -- vector solutions for coplanar forces concurrent  (Page 3/13)

Figure 1 shows the mirror image that is contained in that file for the benefit of your assistant who will create the tactile graphicfor this exercise.

Figure 1 . Mirror image from the file named Phy1100a1.svg.

Figure 2 shows a non-mirror-image version of the same image.

Figure 2 . Non-mirror-image version of the image from the file named Phy1100a1.svg.

Key-value pairs

Figure 3 shows the key-value pairs that go with the image in the file named Phy1100a1.svg.

Create a triangle

Please use your graph board to create a triangle with the dimensions, angles, and labels specified below.

Use your Braille labeler to label the sides of the triangle a, b, and c. Label the angle opposite from side a as A, the angle opposite side b as B, andthe angle opposite side c as C.

Adjust your triangle to make side a equal to 10 units, angle B equal to 80 degrees, and angle C equal to 40 degrees. Using the above relationship, we alsoknow that angle A is equal to 60 degrees because the angles in a triangle must sum to 180 degrees.

Using the law of sines

The law of sines can be used to compute the remaining sides of a triangle when two angles and a side are known. Of course, if you know two of the angles of a triangle, you also know the thirdangle because the sum of the angles in a triangle is always 180 degrees.

Use the Google calculator

All of the arithmetic and trigonometric requirements in this section can be satisfied using the Google calculator. Go to Google and enter the following in the search box:

sine 80 degrees

Google should produce a line of output text that reads:

sine(80 degrees) = 0.984807753

Record this value for future use.

Get and record two more values

Go to Google again and enter sine 40 degrees. The output should be:

sine(40 degrees) = 0.64278761

Doing the same thing again for 60 degrees produces:

sine(60 degrees) = 0.866025404

The law of sines formula

Given the names of the sides and angles that you have applied to your triangle, the law of sines says that the following is true:

(a/sin A) = (b/sin B) = (c/sin C)

In general, the law of sines states that the ratio of the length of any side to the sine of the opposite angle is equal to the ratio of any other side to thesine of its opposite angle.

Compute the length of side b

Substituting the known values in the above formula gives us:

(10/0.866) = (b/0.985) = (c/0.643)

Combining the first and second ratios and rearranging terms gives us:

b = 10 * 0.985/0.866 = 11.4

(You can also use the search box at Google to perform arithmetic such as 10 * 0.985/0.866.)

Compute the length of side c

Combining the first and third ratios and rearranging terms gives us:

c = 10*0.643/.866 = 7.42

Hopefully, you can confirm these values (approximately) by making measurements on the triangle on your graph board.

Another use for the law of sines

The law of sines can also be used when two sides and one of the non-enclosed angles is known to find the values of the other side and the values of the othertwo angles.