SOLUTION: Find the acute angle between the lines whose slopes are 2 and 1÷3

Algebra ->  Points-lines-and-rays -> SOLUTION: Find the acute angle between the lines whose slopes are 2 and 1÷3      Log On


   

Question 1142690: Find the acute angle between the lines whose slopes are 2 and 1÷3
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+alpha+=+arc+tan%28+2+%29+
+beta+=+arc+tan%28+1%2F3+%29+
-------------------------------
+alpha+=+63.435+
+beta+=+18.435+
+63.435+-+18.435+=+45+
45 degrees

Answer by ikleyn(52867) About Me  (Show Source):
You can put this solution on YOUR website!
.

You are given  tan%28alpha%29 = 2  and  tan%28beta%29 = 1%2F3,


and they want you find  acute angle  alpha-+beta.


tan%28alpha+-+beta%29 = %28tan%28alpha%29+-+tan%28beta%29%29%2F%281+%2B+tan%28alpha%29%2Atan%28beta%29%29 = %282-1%2F3%29%2F%281+%2B+2%2A%281%2F3%29%29 = %28%285%2F3%29%29%2F%28%281%2B2%2F3%29%29 = %28%285%2F3%29%29%2F%28%285%2F3%29%29%29 = 1.


Therefore,  alpha+-+beta = pi%2F4 = 45 degrees.    ANSWER

Solved.