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Answer:
<u>0.765 meters</u> long were the sticks when laid end to end.
Step-by-step explanation:
Given:
Rob laid three sticks end to end. The lengths of the sticks were 45 millimeters, 32 centimeters, and 4 decimeters.
Now, to find the length in meters of the sticks when laid end to end.
The lengths of the sticks are:
1st stick - 45 millimeters.
2nd stick - 32 centimeters.
3rd stick - 4 decimeters.
So, we convert the units of sticks into meters by using conversion factor:
1st stick:
1 millimeter = 0.001 meter.
45 millimeters = 0.001 × 45
45 millimeters = 0.045 meter.
2nd stick:
1 centimeter = 0.01 meter.
32 centimeters = 0.01 × 32
32 centimeters = 0.32 meter.
3rd stick:
1 decimeter = 0.1 meter.
4 decimeters = 0.1 × 4
4 decimeters = 0.4 meter.
Now, adding all the three sticks length to get the the length in meters of the sticks when laid end to end:
Therefore, 0.765 meters long were the sticks when laid end to end.
The given angles are
M = 64
N = 48
where P is unknown. While we don't know P at first, we can solve for it. Recall that for any triangle, the three angles always add to 180 degrees
M+N+P = 180
64+48+P = 180
112+P = 180
112+P-112 = 180-112
P = 68
-------------------------------------------
So in summary so far
M = 64
N = 48
P = 68
The shortest side is opposite the smallest angle. The side MP is opposite the smallest angle N = 48
The longest side is going to be opposite the largest angle. In this case, side MN is opposite the largest angle P = 68
The medium side is opposite the medium angle. So NP is the medium side length
-------------------------------------------------------
Final Answers:
Shortest Side = MP
Medium Side = NP
Longest Side = MN
See the attached image for a visual summary
The ascending order would be: MP, NP, MN
Note: Something like MP is the same as PM. The order of endpoints for any given individual segment doesn't matter
M = 64
N = 48
where P is unknown. While we don't know P at first, we can solve for it. Recall that for any triangle, the three angles always add to 180 degrees
M+N+P = 180
64+48+P = 180
112+P = 180
112+P-112 = 180-112
P = 68
-------------------------------------------
So in summary so far
M = 64
N = 48
P = 68
The shortest side is opposite the smallest angle. The side MP is opposite the smallest angle N = 48
The longest side is going to be opposite the largest angle. In this case, side MN is opposite the largest angle P = 68
The medium side is opposite the medium angle. So NP is the medium side length
-------------------------------------------------------
Final Answers:
Shortest Side = MP
Medium Side = NP
Longest Side = MN
See the attached image for a visual summary
The ascending order would be: MP, NP, MN
Note: Something like MP is the same as PM. The order of endpoints for any given individual segment doesn't matter