Question

To find the third side of ABC with AB = 40 cm, BC = 25 cm and BAC = 35°, Velina and Kristian offered the following suggestions: Kristian suggested: "Use the cosine rule as you are given two sides and one angle. Velina suggested: "Use the sine rule as you are given two sides and an angle opposite to one of them." State whose method is correct and justify your statement. Hence, solve the triangle.

Answer 1

Velina is correct.

Explanation:

The side BC is opposite to < BAC so we use the sine rule to find the value of < ACB

25 / sin BAC = 40 / sin ACB

25 / sin 35 = 40 /sin ACB

sin ACB = 40 sin 35 / 25

= 0.917722

< ACB = 66.6 degrees

So the third angle ABC = 180 - 35 - 66.6

= 78.4 degrees.

Now the third side can be found using the sine rule also:

25 / sin 35 = AC / sin 78.4

AC = 25 sin 78.4 / sin 35

= 42.7 cm