Right Angled Triangles

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Presentation transcript:

Right Angled Triangles The key points

Hypotenuse The longest side of a right angled triangle Always opposite the right angle Hypotenuse

Pythagoras’ Theorem The two smaller sides, squared and added together equals the hypotenuse squared. A2 + B2 = C2 Only works for right angled triangles

Find the length of ‘j’ To find ‘j’, use P.T. Label the hypotenuse. j = 9 cm 15cm hyp 12cm j

Any other sort of questions? If it is then the hypotenuse is 6cm (longest side) and P.T. will work. 42 + 52 = 16 + 25 = 41 62 = 36 so 42 + 52 = 62 P.T. does NOT work so no right angle Is this triangle right- angled? Hyp? 4cm 6cm 5cm

So that’s it for right angled triangles?

Don’t forget trigonometry. (Worth big marks) Unfortunately not Don’t forget trigonometry. (Worth big marks)

Key trigonometry facts Trigonometry links the size of the angles to the length of the sides. Only works in right angled triangles. Can be used to find either a length or an angle Don’t forget to check that your calculator is working in degrees.

Help! Label the sides of your triangle Hypotenuse (hyp) - opposite the right angle. Opposite (opp) - opposite the angle you know or want to find. Adjacent (adj) - the remaining side.

Then pick your equation. Sin 0 = opp Cos 0 = adj Tan 0 = opp hyp hyp adj 0 is the Greek letter ‘theta’ which denotes an angle.

But which one should I use? If you are trying to find an angle, work out which two sides you know and use the formula that contains them both. To find a missing side, work out which side you want to find and the side you know and then use the formula which contains both.

What? Find the value of ‘f’ We know the hypotenuse and want to find ‘f’ which is the opposite. We use sin 300 = f / 10 10 x sin 300 = f f = 5cm 10cm ‘f ’ hyp opp 300 adj

Find the value of angle BCA If I call angle BCA, ‘x’ tan x = 4 / 10 = 0.4 so x = tan-1 0.4 x = 21.8o ( to 1 d.p.) A 4cm hyp opp B C 10cm adj

How do I find an angle? obtuse reflex acute

Find the value of 0 Label the sides. We know ‘adj’ and ‘hyp’ so must use cos cos 0 = 5 / 10 cos 0 = 0.5 so 0 = 600 (cos-10.5) 10cm 5cm hyp adj opp

One more for luck! Find the value of ‘P’ Sin 400 = P / 5 5 Sin 400 = P so P = 3.2cm (to 1 d.p.) hyp 5cm P cm opp 400 adj

I don’t want to have to say I hope this helped I don’t want to have to say

That’s all folks! The end