Question

1. choose the law and the formula that would be used to solve the triangle.

law
formula
a. $a^2 = b^2 + c^2 - 2bc \cos a$
b. law of cosines
c. law of sines
d. $b^2 = a^2 + c^2 - 2ac \cos b$
e. $c^2 = a^2 + b^2 - 2ab \cos c$

Explanation:

Step1: Identify the Law

In the triangle, we know two sides (\(c = 4\) cm, \(b = 5.7\) cm) and the included angle (\(\angle A=52^\circ\)). The Law of Cosines is used when we know two sides and the included angle (or three sides) to find a side or an angle. So the law is the Law of Cosines (option b).

Step2: Identify the Formula

The Law of Cosines formula for a triangle with sides \(a\), \(b\), \(c\) and opposite angles \(A\), \(B\), \(C\) respectively is \(a^{2}=b^{2}+c^{2}-2bc\cos A\) when we want to find side \(a\) (opposite angle \(A\)) with known sides \(b\), \(c\) and included angle \(A\). So the formula is option a.

Answer:

Law: b. Law of Cosines
Formula: a. \(a^{2}=b^{2}+c^{2}-2bc\cos A\)