Question

Can you use the Law of Cosines if you are given a = 41, b = 55 and m angleA =56 degrees the measure of angle A equals 56 degrees ? Why or why not?

Answer 1

Quick answer: no you cannot.

Details:

The law of cosines relates between two adjacent sides and the included angle to calculate the third side (opposite to the included angle).

Any combinations of data giving 3 of the above-mentioned pieces of information will enable us to calculate the fourth. Otherwise, the sine rule is used to calculate some of the angles or sides before cosine rule can be used, if at all necessary.

Answer 2

We cannot apply Law of Cosines with given information.

Explanation:

We are asked to determine whether we can use Law of Cosines when
`a=41`,
`b=55` and
`m\angle A=56^(\circ)`.

Law of Cosines relates the two sides and included angle of a scalene triangle to opposite side of included angle.

`a^2=b^2+c^2-2bc\cdot\text{cos}(A)`, where, a, b and c are sides of triangle and A is angle opposite to side a.

We cannot apply Law of Cosines as we have given only two sides and corresponding angle is one of the given sides.

To apply Law of cosines, we need angle opposite to side C or length of side c.

Therefore, we cannot apply Law of Cosines with our given information.