Video: KS2-M16S • Paper 2 • Question 9

Here is a triangle. Measure the shortest side accurately, in centimetres. Measure the largest angle.

05:34

Video Transcript

Here is a triangle. Measure the shortest side accurately, in centimetres. Measure the largest angle.

Now looking at this triangle, this angle here is greater than 90 degrees. These two angles are smaller than 90 degrees. So this angle is the largest angle. And opposite the largest angle, you have the longest side. Now we want to measure the shortest side. So we definitely don’t want to measure the length of the longest side.

Now just looking at the two shorter sides, they look roughly the same length. We’re gonna have to measure both of them in order to see which one is the shortest. So let’s measure the length of this side, this side, and this largest angle. Carefully lay down your ruler so that it’s parallel; it lines up with one of those lines and the zero mark here lines up perfectly with that corner. Then, we can see where the other end of the line goes up to.

Our ruler measures in centimetres: one centimetre, two centimetres, three centimetres, four centimetres, five centimetres, six centimetres, seven centimetres. And these longer lines here tell us where the whole centimetre markings are. Now the space between each whole centimetre is split into 10. So each of those little lines represent a tenth of a centimetre.

Looking at our baseline, it goes from zero on the scale up to six whole centimetres and another seven tenths of a centimetre. So that makes 6.7 centimetres. The baseline of our triangle is 6.7 centimetres long. Now let’s use the same method to measure this other short side.

Carefully line the ruler up with the line with the zero mark at one corner. Then, we need to look carefully where does the next corner line up. It’s five whole centimetres and seven tenths of a centimetre. So that’s 5.7 centimetres. So the shortest side is 5.7 centimetres. Now we’ve measured the shortest side, let’s go on to measure the size of the largest angle.

To measure angles, we need a protractor. Find the baseline between the zeros on your protractor. Make sure you line it up accurately with one of the sides of your triangle. Look carefully for the point on the baseline of your protractor, where the 90-degree line overlaps it. Carefully line up that point with the corner of the triangle that makes the angle you’re trying to measure. Think of this as a target: your target has to line up perfectly with the corner and the baseline of your protractor has to perfectly line up with one of the sides of the triangle.

Notice that you got two sets of numbers going round the outside of your protractor. We’re going to use the scale that starts at zero on the side of the triangle where we’ve lined up our protractor. Now remember it’s this angle here between the two sides of the triangle that we’re trying to measure. So we’re gonna start counting at zero and work our way round that scale until we hit the other side of the triangle.

In this case, we’re going to count through 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, and then a little bit. So our largest angle is 140 degrees plus some more degrees. Now you’ll notice between every 10 degrees, there are 10 little marks or 10 parts. So each one of those little parts represents one degree. If we count the little parts carefully between 140 and where our line is, there are five little parts there. So that represents five degrees.

So our angle measures 140 degrees plus five degrees which is 145 degrees. Now this makes sense because our angle is clearly bigger than 90 degrees, but not as big as 180 degrees. If we’d have used the other scale, we might have said it was somewhere around 40 degrees. And that’s clearly wrong because it’s way less than 90 degrees. So it’s useful to line up your protractor and then just check at the end: does it make sense that it’s roughly that size?

Now just before we go, I’m gonna show you another way of measuring that angle. We could have lined up the baseline of our protractor with the other side of the triangle. We’d still need to carefully line up the crosshair of the protractor with this corner of our triangle. But this time, we’d have started counting from zero on the outer scale. But again, we’d have counted up to 140 and then an extra five degrees but in the other direction.

So either way, the largest angle is 145 degrees.

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