Question

find the measure of each side indicated. round to the nearest tenth.
9)
10)
11)
12)

Explanation:

Problem 9:

Step1: Identify trigonometric ratio

In right triangle \( \triangle ABC \), \( \angle C = 90^\circ \), \( BC = 11 \), \( \angle B = 37^\circ \), and hypotenuse \( AB = x \). We use cosine: \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \), so \( \cos37^\circ=\frac{BC}{AB} \).
\( \cos37^\circ=\frac{11}{x} \)

Step2: Solve for \( x \)

Rearrange to \( x = \frac{11}{\cos37^\circ} \). Using \( \cos37^\circ\approx0.8 \) (approximate value), \( x=\frac{11}{0.8}=13.75\approx13.8 \).

Step1: Identify trigonometric ratio

In right triangle \( \triangle ABC \), \( \angle C = 90^\circ \), \( AC = 13 \), \( \angle A = 32^\circ \), and opposite side \( BC = x \). Use tangent: \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \), so \( \tan32^\circ=\frac{BC}{AC} \).
\( \tan32^\circ=\frac{x}{13} \)

Step2: Solve for \( x \)

Multiply both sides by 13: \( x = 13\times\tan32^\circ \). \( \tan32^\circ\approx0.6249 \), so \( x\approx13\times0.6249\approx8.1 \).

Step1: Identify trigonometric ratio

In right triangle \( \triangle ABC \), \( \angle C = 90^\circ \), \( AC = 5 \), \( \angle A = 50.1^\circ \), and opposite side \( BC = x \). Use tangent: \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \), so \( \tan50.1^\circ=\frac{BC}{AC} \).
\( \tan50.1^\circ=\frac{x}{5} \)

Step2: Solve for \( x \)

Multiply both sides by 5: \( x = 5\times\tan50.1^\circ \). \( \tan50.1^\circ\approx1.199 \), so \( x\approx5\times1.199\approx6.0 \).

Answer:

\( x\approx13.8 \)

Problem 10: