Question

solve for $x$. round to the nearest tenth, if necessary.
image of a right triangle abc with right angle at b, angle at a is 63 degrees, length of bc is 7.5, length of ab is x

Explanation:

Step1: Identify tangent ratio

$\tan(\angle A) = \frac{\text{Opposite side}}{\text{Adjacent side}} = \frac{BC}{AB}$

Step2: Substitute known values

$\tan(63^\circ) = \frac{7.5}{x}$

Step3: Rearrange to solve for $x$

$x = \frac{7.5}{\tan(63^\circ)}$

Step4: Calculate value

$\tan(63^\circ) \approx 1.9626$, so $x \approx \frac{7.5}{1.9626} \approx 3.8$

Answer:

$3.8$