Answer:
= 24.57 to the nearest hundredth
Step-by-step explanation:
The three sides of a right-angled triangle have specific names:
- The hypotenuse (H) is the longest side. It is opposite the right angle.
- The opposite side (O) is opposite the angle in question.
- The adjacent side (A) is next to the angle in question.
The 3 trigonometric ratios are:
![sin(\theta)=\frac{O}{H} \\\\cos(\theta)=\frac{A}{H} \\\\tan(\theta)=\frac{O}{A}](https://tex.z-dn.net/?f=sin%28%5Ctheta%29%3D%5Cfrac%7BO%7D%7BH%7D%20%5C%5C%5C%5Ccos%28%5Ctheta%29%3D%5Cfrac%7BA%7D%7BH%7D%20%5C%5C%5C%5Ctan%28%5Ctheta%29%3D%5Cfrac%7BO%7D%7BA%7D)
For the given triangle we are given the angle, the hypotenuse, and need to find the side that is ADJACENT to the angle.
Therefore, we would use the trig ratio: ![cos(\theta)=\frac{A}{H}](https://tex.z-dn.net/?f=cos%28%5Ctheta%29%3D%5Cfrac%7BA%7D%7BH%7D)
Substituting the values from the triangle: ![cos(35)=\frac{x}{30}](https://tex.z-dn.net/?f=cos%2835%29%3D%5Cfrac%7Bx%7D%7B30%7D)
Multiply both sides by 30: ![30cos(35)=x](https://tex.z-dn.net/?f=30cos%2835%29%3Dx)
Therefore, ![x=24.57456133...](https://tex.z-dn.net/?f=x%3D24.57456133...)
So
= 24.57 to the nearest hundredth