Question

use the diagram to derive the law of cosines. which of the following statements is true?
( b = c cos a )
( x = a cos c )
( c = h cos a )
( \frac { b } { x } = \frac { c } { b } )
done

Explanation:

Step1: Recall the cosine formula in a right - triangle

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).
For the right - triangle with angle \(C\) and hypotenuse \(a\), \(\cos C=\frac{x}{a}\).

Step2: Rearrange the formula

Multiply both sides of the equation \(\cos C = \frac{x}{a}\) by \(a\) to get \(x = a\cos C\).

Answer:

\(x = a\cos C\)