Question

find cd.
write your answer as an integer or as a decimal rounded to the nearest tenth.
cd =
submit

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right triangle \( \triangle BCD \) with \( \angle C = 90^\circ \), \( \angle B = 32^\circ \), and \( BC = 8 \). We need to find \( CD \). We can use the tangent function, which is \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). For \( \angle B \), the opposite side to \( 32^\circ \) is \( CD \), and the adjacent side is \( BC = 8 \). So, \( \tan(32^\circ)=\frac{CD}{8} \).

Step2: Solve for \( CD \)

Multiply both sides by 8: \( CD = 8\times\tan(32^\circ) \). Calculate \( \tan(32^\circ) \approx 0.6249 \). Then \( CD = 8\times0.6249 \approx 4.9992 \approx 5.0 \) (rounded to the nearest tenth).

Answer:

\( 5.0 \)