Question

Mark each statement as True or False?

a) The sine rule is used when we are given either a) two angles and one side, or b) two sides and a non-included angle.
b) The cosine rule is used when we are given either a) three sides or b) two sides and the included angle.

Answer 1

a.True

b. True

Explanation:

a. #Given two angles and one side

Let the given angles be A° and B° and side x, the angle and two remaining sides can be calculated as:

`(a)/(sin \ A\textdegree)=(b)/(sin \ B\textdegree)=(x)/(sin \ (180-A-B)\textdegree)`

#Given two sides and one non-included angle.

Let the given angle A° and sides x and y, the angle remaining sideand angle can be calculated as:

`(x)/(sin \ A\textdegree)=(y)/(sin \ B)=(c)/(sin \ C\textdegree)`

b.#Given three sides

Let the given sides be a, b and c:

The angles can be calculated as:

`a^2=b^2+c^2-2bc\ cos \ A\\\\b^2=a^2+c^2-2ac\ cos \ C\\\\c^2=a^2+b^2-2ab\ cos \ B`

#Given two sides and the included angle

Let the sides given be c, b and the angle A, the remaining sides can be calculated by substituting values in the equation;

`a^2=b^2+c^2-2bc\ cos \ A\\\\`