Question

1. trigonometry

!!!!make sure you are in degree model!!!!
a. put 2 digit numbers in boxes and solve for x. hypotenuse needs to be bigger than the side.

Explanation:

Step1: Use trigonometric ratio (left - hand triangle)

For the left - hand right - triangle, if the angle is \(12^{\circ}\) and the hypotenuse is \(33\). We use the cosine ratio \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here \(\theta = 12^{\circ}\), adjacent side is \(x\), and hypotenuse \(h = 33\). So \(x = h\times\cos\theta\).

$$x=33\times\cos(12^{\circ})$$

$$x = 33\times0.9781$$

(since \(\cos(12^{\circ})\approx0.9781\))

$$x\approx32.28$$

Step2: Use trigonometric ratio (right - hand triangle)

For the right - hand right - triangle, if the angle is \(65^{\circ}\) and the adjacent side is \(11\). We use the cosine ratio \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here \(\theta = 65^{\circ}\), adjacent side \(a = 11\), and hypotenuse is \(x\). So \(x=\frac{a}{\cos\theta}\)

$$x=\frac{11}{\cos(65^{\circ})}$$

Since \(\cos(65^{\circ})\approx0.4226\)

$$x=\frac{11}{0.4226}\approx26.03$$

Answer:

For the left - hand triangle, \(x\approx32\). For the right - hand triangle, \(x\approx26\)