Question

solve for x. round to the nearest tenth, if necessary. answer attempt 1 out of 2 x =

Explanation:

Step1: Identify trigonometric ratio

In right - triangle ABC, we know the side opposite the angle $\angle A$ (BC = 7.5) and we want to find the side adjacent to $\angle A$ (AB = x). We use the tangent function since $\tan(A)=\frac{\text{opposite}}{\text{adjacent}}$. So, $\tan(63^{\circ})=\frac{BC}{AB}$.

Step2: Substitute values

We know that $\tan(63^{\circ})\approx1.9626$ and $BC = 7.5$, $AB=x$. Substituting into the formula $\tan(63^{\circ})=\frac{7.5}{x}$, we can solve for $x$. Rearranging gives $x=\frac{7.5}{\tan(63^{\circ})}$.

Step3: Calculate x

$x=\frac{7.5}{1.9626}\approx3.8$.

Answer:

$3.8$