Answer: 2 cm
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Explanation:
Notice how the angles match up
Angle A = unknown for now
Angle B = 100 degrees, which matches up with angle Q
angle C = 30 degrees which matches up with angle R
As you can probably guess, angle A will match up with angle P. So angle A is 50 degrees.
If we didn't have triangle PQR, then we can still find angle A
A+B+C = 180
A+100+30 = 180
A+130 = 180
A = 180-130
A = 50 degrees
Confirming what was stated earlier.
Because of these angles pairing up, they correspond to one another.
A corresponds to P
B corresponds to Q
C corresponds to R
Therefore, triangle ABC is similar to triangle PQR
The order is very important.
A is the first letter; so is P
B is the second letter; so is Q
C is the third letter; so is R
We want to find the length of PQ. Since P corresponds to A and Q corresponds to B, this means PQ corresponds to AB. They are the first two letters of the sequences PQR and ABC respectively. Similarly, AC corresponds to PR as they are the first and last letters of ABC and PQR respectively
AB = 4 is given
PQ = x is unknown
AC = 8 is given
PR = 4
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So all that set up leads to the proportion
AB/PQ = AC/PR
4/x = 8/4
4*4 = x*8
16 = 8x
8x = 16
x = 16/8
x = 2
So PQ is 2 cm long
