Question

1. the length of the unknown side, to the nearest tenth, is

1. the length of the unknown side, to the nearest tenth, is

1. the length of the unknown side, to the nearest whole number, is

Explanation:

Step1: Recall trigonometric ratio

For a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\)

Step2: Solve problem 4

Given \(\theta = 28^{\circ}\), opposite side \(= 15\mathrm{mm}\), and we want to find the adjacent side \(x\).
Using \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), so \(\tan28^{\circ}=\frac{15}{x}\), then \(x = \frac{15}{\tan28^{\circ}}\).
Since \(\tan28^{\circ}\approx0.5317\), \(x=\frac{15}{0.5317}\approx28.2\)

Step3: Solve problem 5

Given \(\theta = 36^{\circ}\), hypotenuse \(= 45\mathrm{km}\), and we want to find the adjacent side \(x\).
Using \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), so \(\cos36^{\circ}=\frac{x}{45}\), then \(x = 45\times\cos36^{\circ}\).
Since \(\cos36^{\circ}\approx0.8090\), \(x = 45\times0.8090=36.4\)

Step4: Solve problem 6

Given \(\theta = 45^{\circ}\), adjacent side \(= 19\mathrm{cm}\), and we want to find the opposite side \(x\).
Using \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), so \(\tan45^{\circ}=\frac{x}{19}\).
Since \(\tan45^{\circ}=1\), \(x=19\times1 = 19\)

Answer:

1. \(28.2\)
2. \(36.4\)
3. \(19\)