Question

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

Explanation:

9)

Step1: Identify the trigonometric ratio

We know the adjacent side (\(BC = 11\)) and we need to find the hypotenuse (\(AB=x\)). Using the cosine ratio: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here \(\theta = 37^{\circ}\), so \(\cos37^{\circ}=\frac{11}{x}\).

Step2: Solve for \(x\)

$$x=\frac{11}{\cos37^{\circ}}$$

Using \(\cos37^{\circ}\approx0.7986\), we get \(x=\frac{11}{0.7986}\approx13.8\).

10)

Step1: Identify the trigonometric ratio

We know the adjacent side (\(AC = 13\)) and we need to find the opposite side (\(BC=x\)). Using the tangent ratio: \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here \(\theta = 32^{\circ}\), so \(\tan32^{\circ}=\frac{x}{13}\).

Step2: Solve for \(x\)

$$x = 13\times\tan32^{\circ}$$

Using \(\tan32^{\circ}\approx0.6249\), we get \(x=13\times0.6249\approx8.1\).

11)

Step1: Identify the trigonometric ratio

We know the adjacent side (\(AC = 5\)) and we need to find the opposite side (\(BC=x\)). Using the tangent ratio: \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here \(\theta = 50.1^{\circ}\), so \(\tan50.1^{\circ}=\frac{x}{5}\).

Step2: Solve for \(x\)

$$x = 5\times\tan50.1^{\circ}$$

Using \(\tan50.1^{\circ}\approx1.203\), we get \(x=5\times1.203 = 6.0\).

12)

Step1: Identify the trigonometric ratio

We know the hypotenuse (\(AB = 11\)) and we need to find the adjacent side (\(BC=x\)). Using the cosine ratio: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here \(\theta = 60^{\circ}\), so \(\cos60^{\circ}=\frac{x}{11}\).

Step2: Solve for \(x\)

$$x=11\times\cos60^{\circ}$$

Since \(\cos60^{\circ}=0.5\), we get \(x = 11\times0.5=5.5\).

Answer:

1. \(13.8\)
2. \(8.1\)
3. \(6.0\)
4. \(5.5\)