Question

1. 30) 29)

Explanation:

Step1: Recall the trigonometric ratio

For a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). In problem 24, \(\theta = 49^{\circ}\), the opposite side is \(11\) and the adjacent side is \(x\). So, \(\tan(49^{\circ})=\frac{11}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{11}{\tan(49^{\circ})}\). Using a calculator, \(\tan(49^{\circ})\approx1.1504\). Then \(x=\frac{11}{1.1504}\approx9.56\).

For problem 29, using \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here \(\theta = 20^{\circ}\), the hypotenuse is \(10\) and the opposite side is \(x\). So, \(\sin(20^{\circ})=\frac{x}{10}\). Since \(\sin(20^{\circ})\approx0.3420\), then \(x = 10\times\sin(20^{\circ})\approx3.42\).

For problem 30, using \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here \(\theta = 72^{\circ}\), the hypotenuse is \(16\) and the adjacent side is \(x\). So, \(\cos(72^{\circ})=\frac{x}{16}\). Since \(\cos(72^{\circ})\approx0.3090\), then \(x = 16\times\cos(72^{\circ})\approx4.94\).

Answer:

1. \(x\approx9.56\)
2. \(x\approx3.42\)
3. \(x\approx4.94\)