Video: Pack 2 • Paper 2 • Question 7

Pack 2 • Paper 2 • Question 7


Video Transcript

𝐴𝐵𝐶 is a right-angled triangle. Work out the size of angle 𝑥. Give your answer to one decimal place.

So the first thing to do when we’re solving a problem like this is think, okay, what are we gonna use to help us do this? So we can see that it’s a right-angled triangle. So instantly, we go okay, we can use Pythagoras or can use the trig ratios.

Next, we have a look at our triangle. And we can see that, actually, what we’ve got here is an angle. So we’re trying to find an angle. So therefore, we know that we’re actually gonna use our trig ratios, because although we’ve got both sides 𝐴𝐶 and 𝐶𝐵, so therefore we could find 𝐴𝐵 using Pythagoras. The question is actually asking us to find an angle. So we know that it’s gonna be using the trig ratios.

Now whenever solving a problem like this using our trig ratios, I like to follow some basic steps to actually help us make sure that we actually don’t miss out and make any mistakes.

So step one is actually labelling the sides. So the first side that I’ve actually labelled is 𝐻 or the hypotenuse. And this is because it’s the longest side and opposite the right angle. The next side that I’ve actually labelled is the opposite. And that’s 𝐴𝐶, because it’s actually opposite the angle that we’re looking for. And then the final side that I’ve actually labelled is 𝐴, which is 𝐶𝐵. And that’s because that’s the adjacent. And that’s actually adjacent to the angle we’re looking for. Okay, great! So that’s step one complete.

So now step two is to actually choose the ratios. We need to decide which one of our trig ratios we’re actually gonna use to solve the problem. So to actually help us to remember what to do with this, we actually use SOHCAHTOA, because this can actually help us remember our trig ratios.

So we’ve got SOH, which means that the sine of an angle is equal to the opposite divided by the hypotenuse; CAH, which means that the cosine of an angle is equal to the adjacent over the hypotenuse; and TOA, which means the tan of an angle is equal to the opposite over the adjacent.

Okay, so what we need to do is actually choose which one of these ratios we’re going to use. Well, what I’ve actually done is circle the sides that we have. So we have the opposite and the adjacent. So then if we go back to our SOHCAHTOA, we can see, well, it’s TOA that actually has the opposite and the adjacent. So we know that we’re gonna use the tan ratio.

So just to remind us, we’ve got tan 𝜃 is equal to the opposite divided by the adjacent. So then what we’re gonna do is move on to step three. And step three is to actually substitute in our values. So we’ve chosen our ratio. So now we’re gonna substitute in our values. So we get tan 𝑥 is equal to 21, our opposite, divided by 26, which is our adjacent.

So now what we do is we actually move on to our final step, which is step four, which is solve. And the first thing we’re gonna do to actually solve this equation is actually take the inverse tangent or inverse tan of each side of our equation. And when we do that, we get 𝑥 is equal to tan to minus one or inverse tan of 21 over 26.

Well, at this point is to make sure that when you’re actually using a calculator, you press the shift tan button. And that’s how you’d find the inverse of tan. So you press shift and then press tan. Also, another quick thing to actually note here is actually find it easier to put tan to minus one or shift tan of 21 over 26. Don’t try and work out separately because then you might have some errors that are caused by inaccuracy when rounding.

Okay, when we actually calculate this, we get 𝑥 is equal to 38.92754 et cetera degrees. Okay, so if you haven’t got this, you’ll ask yourself why haven’t I got this? I’ve done anything else right. Why haven’t I got this right answer? And that’ll be a very common mistake. And that common mistake is actually that the calculator is in the wrong setting. So you need to make sure that, in the settings, so in the little window we have you display there’s either a d or a capital D or deg, something to noting that actually your calculator is in degrees not radians or anything else.

Okay, so once you’ve done that then you’ll know you’ll get this answer. And so that’s why I said it’s really really important if you’re ever doing any questions or going into an exam, make sure you know your calculator and how it works.

Okay, so now we look back at the question. How do we want our answer left? Well, we can see from the question that we want our answer left to one decimal place. So therefore, we can say that the size of angle 𝑥 is equal to 38.9 degrees to one decimal place.

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