Answer:
Step-by-step explanation:
In Raphael's example, the robot moves in a perfect triangle. A perfect triangle is known to have three equal sides and three equal angles of 60° each. Raphael's example mentions the length of two sides of the triangle as 3m and 4m and it also mentions the angle the robot turns 120°
Therefore the angle created is 180°-120°= 60° which is an angle of a perfect triangle.
The distance that the robot has to calculate would be equal to the length of the third side of the triangle
lets assume the length of the third side of the triangle to be 
and the two remaining angles to be a and b.
To get the distance , let's list out what we know about this triangle.
side a = 3m
side b = 4m
side c =<em> β</em>
Angle 1 = Angle made between side 2 and 3 = A
Angle 2 = Angle made between side 1 and 3 = B
Angle β = Angle made between side 1 and 2 = 60°
The law of cosines states that
= 
+ 
- 2ab(cosβ)
= 
+ 
- 2×3×4(cos 60)
= 9 + 16 - 24(0.5)
= 9 + 16 - 12
= 13
<em>β</em> = 
<em>β</em> = 3.6055512755 m
The distance the robot will compute is 3.61 meter to the nearest hundredth.
Answer:
09:30 AM i hope this helps! :)
Step-by-step explanation:
10:20 -20 minutes = 10:00 - 19 minutes = 09:41 - 11 minutes = 09:30
55 times 30 is 1650 and 30 times 5 is 150
The answer is 1650 over 150
Answer: See explanation
Step-by-step explanation:
a. how old is Cheryl?
Cheryl's age = d + 5
b. how old is Brandon?
d + 5 + 2
= d + 7
c. what was the difference in their ages 5 years ago?
Cheryl age five years ago = d
Brandon's age five years ago = d + 2
Difference = d + 2 - d = 2 years
d. what is the sum of their ages now?
Cheryl's age = d + 5
Brandon age = d + 7
Sum = d + 5 + d + 7
= 2d + 12
e. what will the sum of their ages be two years from now?
Two years from now,
Cheryl's age = d + 5 + 2 = d + 7
Brandon age = d + 7 + 2 = d + 9
Sum = d + 7 + d + 9
= 2d + 16
f. what will the difference of their ages be two years from now
Two years from now,
Cheryl's age = d + 5 + 2 = d + 7
Brandon age = d + 7 + 2 = d + 9
Difference = Brandon age - Cheryl age
= (d + 9) - (d + 7)
= 2 years.
Answer:
x = 11
∠B = 80°
Step-by-step explanation:
∠A =∠B because they are corresponding angles
8x - 8 = 5x + 25
3x = 33
divide both sides of the equation by 3:
x = 11
∠B = 5(11) + 25 = 80°
