Question

solve for x. round to the nearest tenth, if necessary. (image of a right triangle bcd with right angle at c, hypotenuse bd = 30, angle at b is 43 degrees, and side bc = x)

Explanation:

Step1: Identify trigonometric ratio

$\sin(43^\circ) = \frac{x}{30}$

Step2: Solve for x

$x = 30 \times \sin(43^\circ)$

Step3: Calculate value

$x \approx 30 \times 0.6820 = 20.46 \approx 20.5$ (Note: Using calculator for precise $\sin(43^\circ) \approx 0.681998$ gives $30×0.681998≈20.46≈20.5$; if $\sin(43^\circ)$ is approximated as 0.682, result is 20.5)

Wait correction: Rechecking calculator value of $\sin(43^\circ)$ is approximately 0.6819983601, so 30*0.6819983601 ≈20.45995≈20.5 when rounded to nearest tenth. So final answer is 20.5.

Step1: Choose sine function

$\sin(43^\circ) = \frac{x}{30}$

Step2: Rearrange for x

$x = 30 \times \sin(43^\circ)$

Step3: Compute and round

$x ≈ 30×0.6820 ≈20.5$

Answer:

20.8