Answer:
<B = 47°
<C = 28°
b = AC = 28.0
Step-by-step explanation:
Given:
∆ABC
AB = c = 18
BC = a = 37
<A = 105°
Required:
Length of AC = b
measure of angle B and angle C
SOLUTION:
==>Use the sine rule, sin A/a = sinC/c to find the angle of C:
SinA = sin(105) = 0.9659
a = 37
sinC = ?
c = 18
0.9659/37 = sinC/18
Cross multiply
0.9659*18 = 37*sinC
17.3862 = 37*sinC
Divide both sides by 37
17.3862/37 = sinC
0.4699 = sinC
sinC = 0.4699
C = Sin-¹(0.4699)
C = 28.0° (nearest tenth)
==>Find angle B using sum of angles in a triangle:
Angle B = 180 - (105+28)
Angle B = 180 - 133
Angle B = 47°
==>Find length of b using sine rule, b/sinB = c/sinC:
SinC = sin(28) = 0.4695
SinB = sin(47) = 0.7314
c = 18
b = ?
b/0.7314 = 18/0.4695
Cross multiply
b*0.4695 = 18*0.7314
b*0.4695 = 13.1652
Divide both sides by 0.4695
b = 13.1652/0.4695
b = 28.0 (nearest tenth)
The correct option is D.
Option A. isn't even about quadrilater, so we can immediately discard it.
Option B. statement is true, but has nothing to do with the point of the question. In fact, it is true that every square is in particular a rectangle, but in turn every rectangle is a parallelogram. So, there's no counterexample here
Option C. is false, because a dart is a parallelogram: both of its opposite sides are parallel.
Option D. finally presents a counterexample. In fact, The two bases of a trapezoid are parallel, but the two other sides are not. So, a trapezoid is not a parallelogram, even though it has a pair of parallel sides. This is way, in order to be a parallelogram, it is necessary for the quadrilateral to have two pairs of parallel sides.
The decrease in the value of the toy is $9.25 if you subtract $ 0.75 from $10.00 then you get $9.25 so it's $9.25 cheaper
First, you want to establish your equations.
L=7W-2
P=60
This is what we already know. To find the width, we have to plug in what we know into P=2(L+W), our equation to find perimeter.
60=2(7W-2+W)
Now that we only have 1 variable, we can solve.
First, distribute the 2.
60=14W-4+2W
Next, combine like terms.
60=16W-4
Then, add four to both sides.
64=16W
Lastly, divide both sides by 16
W=4
To find the length, we plug in our width.
7W-2
7(4)-2
28-2
L=26
Yes, they're equivalent values.
