Question

fill in the blanks to complete the equation that can be used to solve for the length of side a.
a² = b² + 16² - 2·8·c·cos(d)
a=

b=

c=

d=

Explanation:

Step1: Identify the Law of Cosines

The Law of Cosines for a triangle with sides \(a\), \(b\), \(c\) and the angle \(C\) opposite to side \(c\) is \(a^{2}=b^{2}+c^{2}-2bc\cos(A)\). In the given triangle, we match the values to the formula.

Step2: Determine the values

The side opposite the angle we are using in the cos - term is \(a\). The side adjacent to the given angle of \(49^{\circ}\) with length \(8\) is one of the sides in the formula. Let's assume the side of length \(8\) is \(b\). The other side adjacent to the angle is \(16\), so \(c = 16\), and the angle \(d=49^{\circ}\).

Answer:

a: (unknown side we are solving for)
b: 8
c: 16
d: 49