Question

solve for ( x ). round to the nearest tenth, if necessary.
(there is a right triangle ( bcd ) with right angle at ( c ), hypotenuse ( bd = 30 ), angle at ( b ) is ( 43^circ ), and side ( bc = x ))
answer attempt 1 out of 2
( x = ) input box submit answer

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( BCD \), we know the hypotenuse \( BD = 30 \) and we need to find the adjacent side to angle \( B = 43^\circ \), which is \( BC = x \). The cosine ratio is \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \).
So, \( \cos(43^\circ)=\frac{x}{30} \).

Step2: Solve for \( x \)

Multiply both sides by 30: \( x = 30\times\cos(43^\circ) \).
Calculate \( \cos(43^\circ)\approx0.7314 \), then \( x = 30\times0.7314 = 21.942 \).
Round to the nearest tenth: \( x\approx21.9 \).

Answer:

\( 21.9 \)