SOH CAH TOA - Sin, Cos, Tan

This lesson covers:

  1. How to use the SOHCAHTOA rules to find missing side lengths and angles in right-angled triangles

What do the letters in SOHCAHTOA stand for?


  1. Sin(x)
  2. O
  3. Hypotenuse
  4. C
  5. Adjacent
  6. H
  7. T
  8. Opposite
  9. A
pposite
os(x)
ypotenuse
an(x)
djacent

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5

_____ =Hypotenuse Adjacent​


Which of these correctly completes the above equation?

Tan(x)

Cos(x)

Sin(x)

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1

If we use the 36 ° angle, what is the name of the side labelled a? 

Right triangle with a 36 degree angle and side labeled a.

Opposite

Adjacent

Hypotenuse

0

/

1

If we use the 35 ° angle, what is the name of the side labelled y? 

Right angle triangle with a 35 degree angle and sides labelled 100m and y.

Opposite

Adjacent

Hypotenuse

0

/

1

If we use the 42 ° angle, what is the name of the side labelled y?

Right angle triangle with a 42 degree angle and side labelled y.

Hypotenuse

Opposite

Adjacent

0

/

1

Right angle triangle with a 52 degree angle and a side labeled y to be calculated using SOHCAHTOA.

Calculate the length of side y. Give your answer to 3 significant figures.

(Shapes are not drawn accurately)

8.63

cm

cm

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1

Right angle triangle with sides labelled 3 mm and 8 mm. Angle x is to be calculated.

Calculate the value of angle x. Give your answer to 3 significant figures.

(Shapes are not drawn accurately)

20.6

°

°

0

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1

Right triangle with a 29 degree angle, one side labelled 5 mm, and the other side labelled x.

Calculate the length of side x. Give your answer to 3 significant figures.

(Shapes are not drawn accurately)

2.42

mm

mm

0

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1

Right angle triangle with sides labelled 4.2m and 5.1m, and angle x to be calculated.

Calculate the value of angle x. Give your answer to 3 significant figures.

(Shapes are not drawn accurately)

50.5

°

°

0

/

1

Right-angled triangle with angle 72 degrees at Q and side length 34m at PQ. Calculate the length of side RP.

Calculate the length of side RP. Give your answer to 3 significant figures.

(Shapes are not drawn accurately)

105

m

m

0

/

1

Right angle triangle with an angle of 68 degrees and a side length of 4.8 cm, calculate the length of side x.

Calculate the length of side x. Give your answer to 3 significant figures.

(Shapes are not drawn accurately)

12.8

cm

cm

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1