Question

solve for x. round to the nearest tenth, if necessary. triangle image with right angle at c, side cb = x, angle at b is 43°, hypotenuse db = 30

Explanation:

Step1: Identify trigonometric ratio

For $\angle B = 43^\circ$, side $x$ is adjacent, hypotenuse is 30. Use cosine: $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos(43^\circ) = \frac{x}{30}$

Step2: Isolate $x$

Multiply both sides by 30 to solve for $x$.
$x = 30 \times \cos(43^\circ)$

Step3: Calculate value

Use calculator for $\cos(43^\circ) \approx 0.7314$, compute product.
$x \approx 30 \times 0.7314 = 21.942$

Step4: Round to nearest tenth

Round 21.942 to one decimal place.
$x \approx 21.9$

Answer:

21.9