1. Trigonometry Angles Sides and Lengths Questions Questions Finished
By Heather Eakin

2. 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

3. 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

4. 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!

5. 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

6. 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

7. 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!