Trigonometry Angles Sides and Lengths Questions Questions Finished By Heather Eakin

Angles To work out angles in a (non right angle) triangle you need to use trigonometry which consists of sine, cosine and tangent. Each of these different calculations apply to different parts of the triangle. To remember which parts they apply to use: SOHCAHTOA That is: SineX=Opposite/Hypotenuse CosineX=Adjacent/Hypotenuse and TangentX=Opposite/Adjacent As you can see each of the calculations applies to different sides of the triangle, below is a diagram to show you where each side is on the triangle and how to find it. Hypotenuse-always the longest side X Adjacent-this side is touching/ adjacent to the angle Opposite-this side is opposite to the angle

Angles Explanation! Adjacent X Hypotenuse X Questions To work out the angle of a triangle you need to apply the correct formula so first of all you need to know which sides of the triangle you are using! It’s the hypotenuse and the adjacent, so using SOHCAHTOA you can see we need to use Cosine. X 5cm 6cm 3cm Now we can insert the lengths of the Hypotenuse and Adjacent sides into the formula: CosX=3/6 Finally you must work out the formula: 3/6=0.5 X=0.5/Cos Now click shift and Cos on your calculator to divide 0.5 by Cosine and you are lest with the angle X: X=60 degrees Questions

Angles-Questions X=70.5 X X X=30 X Degrees X=60.25 Explanation Work out angle X for each triangle! X 6cm 2cm X 8cm 4cm X=70.5 X=30 What units do you give your answer to? X 10cm 17.5cm Degrees X=60.25 Explanation Click anywhere for answers!

Lengths To work out lengths in a (non right angle) triangle you need to use trigonometry which consists of sine, cosine and tangent. Each of these different calculations apply to different parts of the triangle. To remember which parts they apply to use: SOHCAHTOA That is: SineX=Opposite/Hypotenuse CosineX=Adjacent/Hypotenuse and TangentX=Opposite/Adjacent As you can see each of the calculations applies to different sides of the triangle, below is a diagram to show you where each side is on the triangle and how to find it. Hypotenuse-always the longest side X Adjacent-this side is touching/ adjacent to the angle Opposite-this side is opposite to the angle

Lengths Explanation! Adjacent X 60 Hypotenuse X 60 Questions To work out the length of a side you need to apply the correct formula so first of all you need to know which sides of the triangle you are using! X 60 It can be either the hypotenuse and the opposite, or the adjacent and the opposite, so using SOHCAHTOA you can see we can use Sine or Tangent. X Now we can insert the lengths of the Hypotenuse and Adjacent sides into the formula: Sin60=X/6 3cm 60 6cm Finally you must work out the formula: Sin60 x 6=X Now click Sin and 60 on your calculator and then multiply by 6 which gives you X: X=5.19cm Questions

Lengths-Questions X=3.73 X X 30 75 X=6.92 Centimetres X 60.25 X=8.68 Work out side X for each triangle! X 6cm 2cm 75 X=3.73 X 8cm 4cm 30 X=6.92 What units do you give your answer to for these questions? X 10cm 17.5cm 60.25 Centimetres X=8.68 Explanation Click anywhere for answers!