Answer:
x = 16°, tan x = 0.3
Step-by-step explanation:
![sin \: 2x = cos \: (3x + 10) \\ cos(90 - 2x) = cos \: (3x + 10) \\ 90 - 2x = 3x + 10 \\ 90 - 10 = 3x + 2x \\ 80 = 5x \\ x = \frac{80}{5} \\ \huge \red{ \boxed{x = 16 \degree }}\\ \\ tan \: x = tan \: 16 \degree \\ = 0.2867453858 \\ = 0.3](https://tex.z-dn.net/?f=sin%20%5C%3A%202x%20%3D%20cos%20%5C%3A%20%283x%20%2B%2010%29%20%5C%5C%20cos%2890%20-%202x%29%20%3D%20cos%20%5C%3A%20%283x%20%2B%2010%29%20%20%5C%5C%2090%20-%202x%20%3D%203x%20%2B%2010%20%5C%5C%2090%20-%2010%20%3D%203x%20%2B%202x%20%5C%5C%2080%20%3D%205x%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B80%7D%7B5%7D%20%20%5C%5C%20%20%5Chuge%20%5Cred%7B%20%5Cboxed%7Bx%20%3D%2016%20%5Cdegree%20%7D%7D%5C%5C%20%20%5C%5C%20tan%20%5C%3A%20x%20%3D%20tan%20%5C%3A%2016%20%5Cdegree%20%20%5C%5C%20%3D%200.2867453858%20%5C%5C%20%20%3D%200.3)
The angle addition postulates states that if an angle UVW has a point S lying in its interior, then the sum of angle UVS and angle SVW must equal angle UVW, or ?UVS + ?SVW= ?UVW.
Number of miles Leeann rode on Day 1 =6.75 miles
Number of miles Leeann rode on Day 2=12.4 miles
The question is asking us to find the total number of miles she rode in all.
Number of miles Leeann rode on Day 1 and day 2 = 6.75+12.4=19.15 miles.
Number of miles she ride her bike both days is 19.5 miles.