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Right Angled Triangles

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

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Right Angled Triangles

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  1. Right AngledTriangles The key points

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

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

  4. Find the length of ‘j’ • To find ‘j’, use P.T. • Label the hypotenuse. • 122 + j2 = 152 144 + j2 = 225 j2 = 81 j = 9 cm 15cm hyp 12cm j

  5. 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? 6cm 4cm 5cm

  6. So that’s it for right angled triangles?

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

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. What? • 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 Find the value of ‘f’ 10cm ‘f ’ hyp opp 300 adj

  13. 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

  14. How do I find an angle? obtuse reflex acute

  15. 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) 0 10cm 5cm hyp adj opp

  16. 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

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

  18. That’s all folks! The end

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