Question

follow these steps to derive the law of cosines.

1. the equation ( a^2 = (b - x)^2 + h^2 ) is expanded to become ( a^2 = b^2 - 2bx + x^2 + h^2 ).
2. using the equation from step 1, the equation ( a^2 = b^2 - 2bx + x^2 + h^2 ) becomes ( a^2 = b^2 - 2bx + c^2 ) by substitution.
3. in ( \triangle abd ), the trigonometric function ( cos(a) = \frac{x}{c} ).
4. multiply both sides of the equation in step 5 by dropdown with a, b, c to get ( x = c cos(a) ).

triangle diagram with labels a, b, c, d, x, ( b - x ), ( h ), ( c ), ( a ), ( b )

Explanation:

Step1: Recall the equation from step 5

The equation from step 5 is $\cos(A)=\frac{x}{c}$.

Step2: Multiply both sides by c

To solve for $x$, we multiply both sides of the equation $\cos(A)=\frac{x}{c}$ by $c$. Using the property of equality (multiplying both sides by the same non - zero number $c$), we get $c\times\cos(A)=c\times\frac{x}{c}$. The $c$ in the numerator and denominator on the right - hand side cancels out, resulting in $x = c\cos(A)$. So we multiply both sides by $c$.

Answer:

c