At a goofy golf course, i need to hit my golf ball into a clown’s mouth that is 3.5 feet above the green. if i am 6.2 feet from the clown cutout, what should my angle of elevation be for the golf ball? a. 29.4 degrees b. 60.6 degrees c. 55.6 degrees d. 34.4 degrees

The answer is the the option a: a.

The explanation for this problem is shown below:

1. You have that the clown’s mouth is above the green and the person is from the clown. Therefore, you have:

The opposite side is and the adjacent side is

2. Now, you can substitute the values and calculate the angle :

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.