Answer:
9. Tan(57°)=~9.24 or 231/25
10. Sin(31°)= ~9.79 or ... 979/100
11. Sin(x°)= 15/23
12. Tan(x°)=37/8
Explanation:
9. For the side length, we must use the given angle and the given side. We want to find the opposite given the adjacent side length of 6. We multiply tan(57°) by 6 using a scientific or graphing calculator and we get the answer 9.24 (after rounding) and then convert to a fraction in simplest form since it asked for a fraction. We would get 231/25
10. Just like the last question, we are given the opposite side length but not the hypotenuse. For this, we use sin. Multiply sin(31°) by 19 and we will getb 9.79 after rounding. Convert this into a fraction and we get 979/100 as the simplest form.
11. For this question we have 2 sides but not the angle. For this, we must use the SOH CAH TOA rule and just connect the pieces. We have the opposite and the hypotenuse or OH which means we have S which is sin. We then write Sin(x°)=15/23
12. For this we have the adjacent and opposite which is OA and that leaves us with T which is Tan(x°)=37/8. Remember that opposite comes before adjacent which is why it isn't 8/37. Hope this helps! (btw I'm not a bot)