In triangle ABC, m∠B = 55, m∠C = 100, and AC = 6. To the nearest tenth, what is the length of AB¯¯¯¯¯¯

|AB|= 7.2 to the nearest tenth

Step-by-step explanation:

If <ACB=100 degrees, <ABC=55 degrees and |AC|=6,

REFER TO THE DIAGRAM 1.1 ATTACHED

In a triangle, the angles are labelled using capital letters and the opposite corresponding sides by small letters as seen in Diagram 1.2.

The Sine and Cosine rule are used to find missing length and angles in triangles.

The Sine Rule is used when we are given two lengths and an angle opposite one of the given lengths or two angles and a side.

The Cosine rule is used when the Sine Rule fails.

The Sine Rule is:

a/Sin A= b/Sin B = c/Sin C

Hence |AC|=b, |AB|=c

b/Sin B = c/Sin C

6/sin 55= c/sin 100

Cross Multiplying

c* sin 55 = 6* sin 100

c= (6* sin 100)/sin 55

|AB|=c = 7.21336967816

|AB|= 7.2 to the nearest tenth

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step-by-step explanation: