Given:
The measure of three sides of a triangle are 8, 7 and 14.
To find:
The measure of the angle opposite the side of length 8.
Solution:
According to the Law of Cosine:
Let a=8, b=7 and c=14, then by using Law of Cosine, we get
Taking cos inverse on both sides.
Therefore, the measure of the angle opposite the side of length 8 is 22.6 degrees.
Answer:
20.9
Step-by-step explanation:
Answer:
( 2,1) is the center of dilation and -2 is the scale factor
Step-by-step explanation:
We can use the formula
A' = k( x-a) +a, k( y-b)+b where ( a,b) is the center of dilation and k is the scale factor
(0,0) becomes (6,3)
( 6,3) = k( 0-a) +a, k( 0-b)+b
6 = -ka+a
3 = -kb+b
We also have
(4,0) becomes (-2,3)
( -2,3) = k( 4-a) +a, k( 0-b)+b
-2 =4k -ka+a
3 = -kb+b
Using these two equations
6 = -ka+a
-2 =4k -ka+a
Subtracting the top from the bottom
-2 =4k -ka+a
-6 = ka -a
-------------------
-8 = 4k
Divide by 4
-8/4 = 4k/4
-2 = k
Now solving for a
6 = -ka +a
6 = - (-2)a +a
6 = 2a+a
6 = 3a
Divide by 3
6/3 =3a/3
2=a
Now finding b
3 = -kb+b
3 = -(-2)b+b
3 = 2b+b
3 = 3b
b=1
The team plays 20 matches.
65% of the matches, the teams wins
= 20 * 0.65
= 13 matches
15% of the matches, the games ends in draw.
= 20 * 0.15
= 3 matches
The team is expected to lose in
= 20 - 13 - 3
= 4 matches
Answer: m∠BCE = 63°
m∠BAD = 76°
Step-by-step explanation:
Problem 1:
Given
m∠BEC = 90°
m∠EBC = 27°
Total = 117°
Solution:
Subtract 180° - 117° = m∠BCE = 63°
Problem 2:
Given
m∠ADE = 52°
m∠ABE = 52°
Total = 104°
Solution:
Subtract 180° - 104° = m∠BAD = 76°
