Given a triangle with a = 9, b = 11, A = 31°, what is (are) the possible length(s) of c? Round your answer to two decimal places
.
A) 16.42 or 2.44
B) 6.61
C) 14.21
D) 16.42 or 3.41
A) 16.42 or 2.44
B) 6.61
C) 14.21
D) 16.42 or 3.41
1 answer:
You can use the Law of Cosines to figure this.
a² = b² +c² -2bc×cos(A)
c² -(2b×cos(A))c +b² -a² = 0
c² -18.8577c +40 = 0 . . . . . . . substituting the given values
Then we can use the quadratic formula to find c.
c = (18.8577 ±√(18.8577² -160))/2
c = (18.8577 ±13.9861)/2 ≈ {2.44, 16.42}
The appropriate choice is ...
A) 16.42 or 2.44
a² = b² +c² -2bc×cos(A)
c² -(2b×cos(A))c +b² -a² = 0
c² -18.8577c +40 = 0 . . . . . . . substituting the given values
Then we can use the quadratic formula to find c.
c = (18.8577 ±√(18.8577² -160))/2
c = (18.8577 ±13.9861)/2 ≈ {2.44, 16.42}
The appropriate choice is ...
A) 16.42 or 2.44
You might be interested in
We know that
case a)
the equation of the vertical parabola write in vertex form is
y=a(x-h)²+k,
where (h, k) is the vertex.
Using our vertex, we have:
y=a(x-2)²-1
We know that the parabola goes through (5, 0),
so
we can use these coordinates to find the value of a:
0=a(5-2)²-1
0=a(3)²-1
0=9a-1
Add 1 to both sides:
0+1=9a-1+1
1=9a
Divide both sides by 9:
1/9 = 9a/9
1/9 = a
y=(1/9)(x-2)²-1
the answer is
a=1/9
case b)
the equation of the horizontal parabola write in vertex form is
x=a(y-k)²+h,
where (h, k) is the vertex.
Using our vertex, we have:
x=a(y+1)²+2,
We know that the parabola goes through (5, 0),
so
we can use these coordinates to find the value of a:
5=a(0+1)²+2
5=a+2
a=5-2
a=3
x=3(y+1)²+2
the answer is
a=3
see the attached figure
case a)
the equation of the vertical parabola write in vertex form is
y=a(x-h)²+k,
where (h, k) is the vertex.
Using our vertex, we have:
y=a(x-2)²-1
We know that the parabola goes through (5, 0),
so
we can use these coordinates to find the value of a:
0=a(5-2)²-1
0=a(3)²-1
0=9a-1
Add 1 to both sides:
0+1=9a-1+1
1=9a
Divide both sides by 9:
1/9 = 9a/9
1/9 = a
y=(1/9)(x-2)²-1
the answer is
a=1/9
case b)
the equation of the horizontal parabola write in vertex form is
x=a(y-k)²+h,
where (h, k) is the vertex.
Using our vertex, we have:
x=a(y+1)²+2,
We know that the parabola goes through (5, 0),
so
we can use these coordinates to find the value of a:
5=a(0+1)²+2
5=a+2
a=5-2
a=3
x=3(y+1)²+2
the answer is
a=3
see the attached figure