Question

552 = 502 + 352 − 2(50)(35)cos(A) After working through the problem above, we get cos(A) = .

Answer 1

We have been given an equation $55^2=50^2+35^2-2(50)(35)\text{cos}(A)$. We are asked to find the values of $\text{cos}(A)$.

First of all, we will square the terms.

$3025=2500+1225-3500\text{cos}(A)$

$3025=3725-3500\text{cos}(A)$

Now we will subtract 3725 from both sides as:

$3025-3725=3725-3725-3500\text{cos}(A)$

$-700=-3500\text{cos}(A)$

Switch sides:

$-3500\text{cos}(A)=-700$

Upon dividing both sides by $-3500$, we will get:

$\frac{-3500\text{cos}(A)}{-3500}=\frac{-700}{-3500}$

$\text{cos}(A)=\frac{7}{35}$

$\text{cos}(A)=\frac{1}{5}$

$\text{cos}(A)=0.2$

Therefore, the values of $\text{cos}(A)$ is 0.2.