You are given the equation \sqrt{76+n } and \sqrt{2n + 26}. What is the smallest value of n that will make each number rational?
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Answer:
Step-by-step explanation:
From the diagram:
Now Angle 1 and Angle 2 are on a straight line, therefore:
You can first find the values of each of the function individually and add the two function up.
I will first reveal the most obvious secret of trig: Most of the problems are 30/60/90 or 45/45/90 triangles of some sort.
The rule to remember is
has solutions
integer 
Continuing where we left off, a cosine of -1/2 is a 30/60/90 triangle in the second or third quadrant; we pick second, and a little thought tells us the angle is
.
integer
In the range we want, that's
with the plus sign and 
with the minus, so
or 
or 
The rule to remember is
Continuing where we left off, a cosine of -1/2 is a 30/60/90 triangle in the second or third quadrant; we pick second, and a little thought tells us the angle is
In the range we want, that's