Drawing a diagram of a triangle may be helpful. The hypotenuse is irrelevant, but the vertical leg and the horizontal leg are useful. Since we know the engineer is looking up at a 45 degree angle from a distance of 200 feet, we can label the vertical leg the "opposite", since it is on the opposite side of the angle we are given. The horizontal leg then becomes the "adjacent". You can then use trigonometry to solve for the opposite.
The options are:
sin(theta)= opposite/hypotenuse
cos(theta)= adjacent/hypotenuse
tan(theta)= opposite/adjacent
Since we don't care about the hypotenuse, the last equation is the one to use. The angle we are given can be substituted in for theta:
tan(45)= x/200
1.61977519= x/200
x= 323.955038 feet
Multiply both the numerator and denominator by
, which is called the "conjugate" of
:

Why do we pick this number? Recall the difference of squares factorization:

Now replace
and
. Then

So in your fraction, you end up with

Finally, just expand the product.

Answer:
The value of x is -2 and 2.
Step-by-step explanation:
When solve an expression, you have to make the expression equals to 0 by moving all the terms to one side :
x² - 3x - 1 = -3x + 3
x² - 3x - 1 + 3x - 3 = 0
x² - 4 = 0
Next, you have to factorize and solve it :
x² - 4 = 0
x² + 2x - 2x - 4 = 0
x(x + 2) - 2(x + 2) = 0
(x + 2)(x - 2) = 0
x + 2 = 0
x = -2
x - 2 = 0
x = 2