Answer:
Step-by-step explanation:
21)
The sine rule is expressed as
a/SinA = b/SinB = c/SinC
Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Therefore,
12/Sin 64 = x/Sin 12
Cross multiplying, it becomes
xSin 64 = 12Sin12
xSin 64 = 12 × 0.209
0.8988x = 2.508
x = 2.508/0.8988
x = 2.79
The sum of the angles in a triangle is 180 degrees. Therefore, the unknown angle in triangle is
180 - (64 + 12) = 104 degrees. Therefore,
y/Sin104 = 12/Sin64
ySin64 = 12Sin104
0.8988y = 12 × 0.9703 = 11.6436
y = 11.6436/0.8988
y = 12.95
22) we would apply the law of Cosines which is expressed as
a² = b² + c² - 2bcCosA
Therefore,
28² = 20² + 24² - 2 × 20 × 24Cosx
784 = 400 + 576 - 960Cosx
784 = 976 - 960Cosx
960Cosx = 976 - 784 = 192
Cosx = 192/960 = 0.2
x = Cos^(-1)0.2
x = 78.5°
I saw the image that should have been included in this problem.
It was a rectangular prism. It can also be identified as a right prism because its bases are aligned one directly above the other and its lateral faces are rectangular.
The image has the following measurements:
length = 7 inches
width = 5 inches
height = 4 inches
volume = length * width * height
v = 7 in * 5 in * 4 in
v = 140 in³ Choice B i believe.
We know that
if the dilated circle <span>passes through the point (4, 0)
so
the new radius is the distance from the origin to point (4,0)
d=</span>√[(4-0)²+0²]-----> d=√16------> d=4 units
the new radius is 4 units
original radius is 1 units
[new radius]=[scale]*[original radius]
scale=new radius/original radius-----> scale=4/1-----> 4
the answer is
<span>the scale factor of dilation is 4</span>