Question

solve for x.
image of a right triangle with right angle at c, angle at the other acute vertex is 32 degrees, side ac is 46, side bc is x
x = \boxed{} (round to the nearest hundredth.)

Explanation:

Step1: Identify trigonometric ratio

We use tangent: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

$\tan(32^\circ) = \frac{x}{46}$

Step3: Solve for x

$x = 46 \times \tan(32^\circ)$

Step4: Calculate and round

$\tan(32^\circ) \approx 0.6249$, so $x \approx 46 \times 0.6249 = 28.7454$
Round to nearest hundredth: $x \approx 28.75$

Answer:

28.75