SOLUTION: Just two more problems on this worksheet and i will be finished with my homework! Please help. Thanks in advance. #3: Find x. image: http://prntscr.com/6ixnmq and #20: P

Algebra ->  Triangles -> SOLUTION: Just two more problems on this worksheet and i will be finished with my homework! Please help. Thanks in advance. #3: Find x. image: http://prntscr.com/6ixnmq and #20: P      Log On


   



Question 957138: Just two more problems on this worksheet and i will be finished with my homework! Please help. Thanks in advance.
#3: Find x. image: http://prntscr.com/6ixnmq
and
#20: Pete is building a kite. Find the measure of the angle the 2-foot edge makes with the 3-foot edge. image: http://prntscr.com/6ixovz

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
.
#3: Using the Pythagorean theorem,
Y%5E2%2B2%5E2=X%5E2
X%5E2%2BZ%5E2=9%5E2
Y%5E2%2B7%5E2=Z%5E2
Let's use a substitution,
a=Y%5E2
b=X%5E2
c=Z%5E2
So,
1.a%2B4=b
2.b%2Bc=81
3.a%2B49=c
Substituing 1 into 2,
a%2B4%2Bc=81
4.a%2Bc=77
From 3,
5.a-c=-49
Add 4 and 5,
a%2Bc%2Ba-c=77-49
2a=28
a=14
Then,
14%2Bc=77
c=63
and
b%2B63=81
b=18
So back substituting,
Y%5E2=14
Y=sqrt%2814%29
.
.
X%5E2=18
X=sqrt%2818%29
X=3sqrt%282%29
.
.
Z%5E2=63
Z=sqrt%2863%29
Z=3sqrt%287%29
.
.
.
.
Using the law of cosines,
4%5E2=2%5E2%2B3%5E2-2%282%29%283%29cos%28C%29
cos%28C%29=%2816-4-9%29%2F%28-12%29
cos%28C%29=-1%2F4
C=104.5