Here’s a question that really requires a calculator, but not until a late
problem-solving stage:
What you have here is essentially a quadratic equation in which the unknown
is tan x. For simplicity’s sake, substitute y for tan x:
Now solve for y:
Now you know that tan x = 3 or –2. Since x is a positive acute angle, the
tangent is positive, and tan x = 3. Now’s the time to use your calculator. You
want to know what acute angle has a tangent of 3. In other words, what you’re
If 0° < x < 90°, and tan^2 x − tanx = 6, which of the following could be
the value of x in degrees (rounded to the nearest degree)?