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 …

Question

asked Mar 10, 2021 190k views

1 Answer

Thomas Piard · Answer 1 · 2021-03-15T16:22:44+0000

Answer:

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;

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