There isn't a picture to answer the question fully
22 feet. Using the sine rule theory: 20/sin(65)=x/sin(90). You know that it's 90 degrees because you assume the ground and the building make a 90 degree angle. So, you cross multiply and get 20sin(90)/xsin(65) and solve for x.
Pi/4 radians
You're looking for the angle that has a secant of sqrt(2). And since the secant is simply the reciprocal of the cosine, let's take a look at that.
sqrt(2) = 1/x
x*sqrt(2) = 1
x = 1/sqrt(2)
Let's multiply both numerator and denominator by sqrt(2), so
x = sqrt(2)/2
And the value sqrt(2)/2 should be immediately obvious to you as a trig identity. Namely, that's the cosine of a 45 degree angle. Now for the issue of how to actually give you your answer. There's no need for decimals to express 45 degrees, so that caveat in the question doesn't make any sense unless you're measuring angles in radians. So let's convert 45 degrees to radians. A full circle has 360 degrees, or 2*pi radians. So:
45 * (2*pi)/360 = 90*pi/360 = pi/4
So your answer is pi/4 radians.
2 pairs of lines that intersect
So from what I understand, you would multiply 10m by 5m for the width to get 50m squared, and multiply the 50 by 2 to get 100m for both sides of the width for the pool. Next the length. Multiply 25m by 2.5m to get 62.5m squared. Once again, mutiply it by 2 for both side lengths of the pool to get 125m. Last, add 125m and 100m to get 225m for the concrete border of the pool.
