Trigonometry & pythagoras help please!

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Zoe Lea
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When do you use Trigonometry? Is it when you need to find the angle of a right angle triangle? If so how do I work out the angles of other triangles or the length of a right angle triangle? When do I use Pythagoras? Please can someone explain!
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2771024
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You use Pythagoras to find a missing length on a right angled triangle.

Use the formula:

a^2 + b^2 = c^2

C is always the hypotenuse. The hypotenuse is always opposite the right angle.
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blabla98875
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Trig is for right-angled triangles, to find lengths of sides and sizes of angles. However, as you will find out at Grade 7/8 GCSE (and Maths A Level), trig can also be used for non-right-angled triangles too.

To work out in trig..remember SOHCAHTOA. Your teacher really should explain that simply.

Pythagoras also can be used to work out lengths of Right-angled triangles, using a^2 + b^2 = c^2
Where c = hypotenuse (longest side),
a and b are the other 2 sides.

A way you could work out length of non-right-angled triangles is;
eg if you had an equilateral triangle, make it into 2 right-angled triangles and use a method to solve.



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Tombre
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Trig is used for right angled triangles.
A good place to start would be to label the triangle. You should have an angle given or perhaps one you need to find. The side opposite that angle is opposite, the longest side is the hypotenuse and the one left is the adjacent.
You can use SOH CAH TOA to find lengths and angles, you can rearrange to find sides or if you need to find an angle and you're given sides, you rearrange by pressing the shift button on your calculator and then the function you need (S, C or T) and then doing the e.g. opposite / adjacent within the brackets of the function.
Pythagoras is to find sides only.

To find sides or angles of non-right-angled triangles, if you do higher tier then you will be introduced to the sine and cosine rules.

Sine Rule: a / SinA = b / SinB = c / Sin C

Cosine Rule: a^2 = b^2 + c^2 - 2bcCosA

where lowercase letters = sides and capital letters = angles. The two letters the same are the angle and side opposite each other.

If you don't do higher tier then I don't think you need to worry about finding sides of non-right-angled triangles
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B_9710
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Pythagoras' theorem states the relationship between the sides of any right angle triangle (in the plane at least ). The (main) trigonometric functions,  \sin , \cos , \tan relate two sides and an angle in a right angle triangle using what you've probably heard said as SOHCAHTOA.
That being said there is the cosine rule and the sine rule which extend these notions to any triangle, not just one with a right angle.
It's hard to just give a generic way of saying which one to use, you have to practice problems with triangles and figure it out on your own I think.
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Isaac Caletrio
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Has no one ever been taught the cool way of remembering sin cos tan? SexOnHoliday CausesAHeadache TakeOneAspirin
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Normaleila
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Hi Zoe Lea
I think some of these replies may confuse you. Not because they're wrong - just a bit 'high level'.
I got an A in Maths two years ago - without ever mastering trigonometry. I do understand Pythagoras' theorem - which is why I recommend you master that first.
If you know the lengths of two sides of a right angled triangle, the theorem lets you work out the length of the third side. If you are told the length of all three sides, you can use the theorem to decide whether he triangle is indeed a right-angled triangle.
The theorem says that the square on the hypotenuse is equal to the sum of the squares on the other two sides. Unfortunately that doesnt mean much until it's explained!
Draw a horizontal line 4 cm long. From one end, draw a vertical line 3 cm long. You have drawn a right angle - and the two lines are called a and b.
Now draw a line from the end of a to the end of b. You have drawn a triangle. The third side is the longest side and it is called c or the hypotenuse. The hypotenuse is opposite the right angle.
The next step is to use each side of the triangle to draw 3 squares. The square with line a as the base has sides of length 4 cm (obviously) and the square with line b as its base has sides 3 cm long. How long is the hypotenuse ? Trust me, it's 5 cm. Draw the square with sides 5 cm long. If you covered each square with 'tiles' of 1 cm x 1 cm, you'd use:
16 to cover square a,
9 to cover square b,
25 to cover square c (the square on the hypotenuse ).
What have you just proved? That in a right-angled triangle with sides of 3, 4 and 5, the square of the hypotenuse (25) equals the sum of the squares of the other two sides (16 +9). Trust me, this is always true IF it's a right-angled triangle.
Once you really undestand and believe this rule, you have learned Pythagoras theorem.
Just remember 3, 4, 5. 9 + 16 = 25.
If the hypotenuse is 5 and one side is 4, then the other side must be 3.
Imagine a triangle with sides of 5, 6 and 9 cm. Is it a right-angled triangle ? No, it cant be, because:
5 x 5 = 25.
6 x 6 = 36.
9 x 9 = 81.
And 25 + 36 doesn't equal 81.
I hope this helps.
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Normaleila
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(Original post by Normaleila)
Hi Zoe Lea
I think some of these replies may confuse you. Not because they're wrong - just a bit 'high level'.
I got an A in Maths two years ago - without ever mastering trigonometry. I do understand Pythagoras' theorem - which is why I recommend you master that first.
If you know the lengths of two sides of a right angled triangle, the theorem lets you work out the length of the third side. If you are told the length of all three sides, you can use the theorem to decide whether he triangle is indeed a right-angled triangle.
The theorem says that the square on the hypotenuse is equal to the sum of the squares on the other two sides. Unfortunately that doesnt mean much until it's explained!
Draw a horizontal line 4 cm long. From one end, draw a vertical line 3 cm long. You have drawn a right angle - and the two lines are called a and b.
Now draw a line from the end of a to the end of b. You have drawn a triangle. The third side is the longest side and it is called c or the hypotenuse. The hypotenuse is opposite the right angle.
The next step is to use each side of the triangle to draw 3 squares. The square with line a as the base has sides of length 4 cm (obviously) and the square with line b as its base has sides 3 cm long. How long is the hypotenuse ? Trust me, it's 5 cm. Draw the square with sides 5 cm long. If you covered each square with 'tiles' of 1 cm x 1 cm, you'd use:
16 to cover square a,
9 to cover square b,
25 to cover square c (the square on the hypotenuse ).
What have you just proved? That in a right-angled triangle with sides of 3, 4 and 5, the square of the hypotenuse (25) equals the sum of the squares of the other two sides (16 +9). Trust me, this is always true IF it's a right-angled triangle.
Once you really undestand and believe this rule, you have learned Pythagoras theorem.
Just remember 3, 4, 5. 9 + 16 = 25.
If the hypotenuse is 5 and one side is 4, then the other side must be 3.
Imagine a triangle with sides of 5, 6 and 9 cm. Is it a right-angled triangle ? No, it cant be, because:
5 x 5 = 25.
6 x 6 = 36.
9 x 9 = 81.
And 25 + 36 doesn't equal 81.
I hope this helps.
Having trouble posting this. Hope it gets posted this time.
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