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As a baisc rule, you use Pythagorus when there are no angles given in the question. If there are angles shown then you should use Trigonometry.
Q 19.1 (Paper 1 2023) Figure 13 shows the cross section of a tree trunk that is going to be sawn into planks as illustrated.
To answer this question you will need to use Pythagorus as there are no angles given.
STep 1: Understand what the question is asking you and think through what rule to use
STep 1: Understand what the question is asking you and think through what rule to use
You can visibly see that Plank A is close to the diameter of the log (circle). To find the length of A we can use what we visibly see i.e. that the bottom of the plank touches the circumference of the log (circle). Therefore if we draw a line from that point to the centre of the log (circle) then we have the Radius of the Log (circle). The diameter of the Log (circle) is given as symbol 140mm, therefore the Radius will be 70mm. You also know that the height of the plank is 15mm so you know two measurements, but no angles, therefore you use Pythagorus. You can use the two given measurements to apply a Pythagorus ratio. For this question you will need to find the Opposite side length so the correct formula to use will be a2 + b2 = c2.
step 2: applying the formula
step 2: applying the formula
a2 + b2 = c2
Find which is the largest area (length of side). In this case it is 70. The other two areas must add up to c2 (70mm squared). Therefore c2 = a2 + b2.
70 x 70 = a2 + b2
4900 = 15 x 15 +b2
4900 = 225 + b2
4900 - 225 = b2
4675 = b2
square root of 4675 = b
b = 68.37mm
therefore the length of the plank is 68.37 x 2 = 136.74mm
step 3: presenting the answer in SF
step 3: presenting the answer in SF
137mm
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