Presentation on theme: "Right AngledTriangles Right Angled Triangles The key points."— Presentation transcript:
Right AngledTriangles 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. A 2 + B 2 = C 2 Only works for right angled triangles
Find the length of j To find j, use P.T. Label the hypotenuse j 2 = j 2 = 225 j 2 = 81 j = 9 cm 15cm 12cm j hyp
Any other sort of questions? If it is then the hypotenuse is 6cm (longest side) and P.T. will work = = = 36 so = 6 2 P.T. does NOT work so no right angle Is this triangle right- angled? 4cm 5cm 6cm Hyp?
So thats it for right angled triangles?
Unfortunately not Dont 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 Dont 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? We know the hypotenuse and want to find f which is the opposite. We use sin 30 0 = f / x sin 30 0 = f f = 5cm 10cm f adj 30 0 opp hyp Find the value of f
Find the value of angle BCA If I call angle BCA, x tan x = 4 / 10 = 0.4 so x = tan x = 21.8 o ( to 1 d.p.) B A C 10cm 4cm hyp adj opp
How do I find an angle? obtuse acute reflex
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 = 60 0 (cos ) 0 10cm opp 5cm adj hyp
One more for luck! Find the value of P Sin 40 0 = P / 5 5 Sin 40 0 = P so P = 3.2cm (to 1 d.p.) 5cm P cm 40 0 opp adj hyp