I'll answer the first four problems.
-----------------------------------------------------------
Problem 33)
s = 10 is the given side length
d = unknown is the diagonal
s^2+s^2 = d^2
2*s^2 = d^2
2*(10)^2 = d^2
d^2 = 200
d = sqrt(200)
d = 14.142135623731
d = 14.1
The diagonal is approximately 14.1 cm long
-----------------------------------------------------------
Problem 34)
I'm assuming the angle says "16 degrees" (The text is a bit small). If this assumption is wrong, then let me know. Thanks.
tan(angle) = opp/adj
tan(16) = 200/x
x*tan(16) = 200
x = 200/tan(16)
x = 697.482888768181
x = 697
The boat is about 697 feet away from the base of the cliff
-----------------------------------------------------------
Problem 35)
sin(A) = sin(30) = 1/2
cos(A) = cos(30) = sqrt(3)/2
tan(A) = tan(30) = sin(30)/cos(30)
tan(A) = tan(30) = (1/2)/(sqrt(3)/2)
tan(A) = tan(30) = (1/2)*(2/sqrt(3))
tan(A) = tan(30) = 1/sqrt(3)
tan(A) = tan(30) = sqrt(3)/3
So in short,
sin(A) = 1/2
cos(A) = sqrt(3)/2
tan(A) = sqrt(3)/3
-----------------------------------------------------------
Problem 36)
The measure of an inscribed angle equals half of that of the central angle.
