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Using trigonometry to find the size of one of the angles in a right-angled triangle
Suppose we want to find the size of the angle marked as x. We can use trigonometry if we know the lengths of two of the sides of the triangle.
Looking at where x is we can label the sides hyp, opp and adj.
If the angle x was at the top then adj and opp would swap places - look at the diagram below.
Depending on which two sides we know, we would use Sin, Cos or Tan. So if we know the lengths of opp and hyp we use Sin, adj and hyp is Cos, opp and adj is Tan (Soh Cah Toa).
We use it like the example below:
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If angle A is the one we are looking at then, 4 cm is the opp and 7 cm is the hyp. |
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This means that it is a Sin question |
If I work out the opp
) hyp it gives me the Sin of angle A.We write it like this :
|
Sin A |
= |
opp |
|
|
|
hyp |
|
Sin A |
= |
4 |
= |
0.57143 (to 4 dp) |
|
|
|
7 |
|
|
Now I know what the Sin of angle A is, I can use my calculator to find the angle itself.
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A = inv. Sin 0.57143 |
(I do this using the Shift key on the calculator) |
So A = 34.8499
E (to 4 dp)Do it yourself on the calculator to check that you get the same answer. If you don't - check that your calculator has a small D or Deg on the screen not R, G, Rad or Grad. If you see one of those four you will have to change the mode on your calculator.
If this works okay, you can find angles using trigonometry.
Now go back to the white workbook and try these questions from Page 58.
Qu. 1 (c), (e), (f)
Qu. 2 (i)
Qu. 3 (n), (p)
Qu. 4 (u), (v)