Trigonometry: finding a side

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Last lesson. Find x to 1 decimal place.

a

4.8 cm

b

8.0 cm

c

6.1 cm

You stand 25 m from a tree.
How could you find its height?

SOHCAHTOA

sin θ = OH

cos θ = AH

tan θ = OA

Finding a side

  1. Labelonly the two sides you use, from the angle.
  2. PickSOH, CAH or TOA.
  3. Writethe ratio with the numbers in.
  4. RearrangeMake the unknown the subject of the formula.
  5. Calculateand round as asked.
Walkthrough to print

Which side is the opposite?

q

Label the two sides with O, A or H: the one you know and the one you are trying to find.

35°12 cmx50°x8 cm28°x6.5 m42°15 cmx57°x9.2 m31°4 cmx46°20 mmx61°7.4 cmxHOOAHOHAHAOAHOOA

cos θ = AH

Label only the two sides you use.
SOHCAHTOA
cos 35° = x11
x = 11 × cos 35°
x = 9.0 cm
SOHCAHTOA
cos 52° = x8
x = 8 × cos 52°
x = 4.9 cm
Label only the two sides you use.
SOHCAHTOA
cos 35° = x11
x = 11 × cos 35°
x = 9.0 cm
SOHCAHTOA
cos 27° = 9x
x = 9 ÷ cos 27°
x = 10.1 cm

Using cosine. Find x to 1 decimal place.

●○○
1

8.2 cm

2

9.2 cm

3

3.2 cm

●●○
1

5.9 cm

2

7.9 cm

3

2.6 cm

●●●
1

14.1 cm

2

9.0 cm

3

5.5 cm

tan θ = OA

Label only the two sides you use.
SOHCAHTOA
tan 38° = x9
x = 9 × tan 38°
x = 7.0 cm
SOHCAHTOA
tan 24° = x6.5
x = 6.5 × tan 24°
x = 2.9 cm
Label only the two sides you use.
SOHCAHTOA
tan 38° = x9
x = 9 × tan 38°
x = 7.0 cm
SOHCAHTOA
tan 55° = 14x
x = 14 ÷ tan 55°
x = 9.8 cm
Label only the two sides you use.
SOHCAHTOA
tan 38° = x9
x = 9 × tan 38°
x = 7.0 cm
SOHCAHTOA
cos 41° = x12
x = 12 × cos 41°
x = 9.1 cm
Label only the two sides you use.
SOHCAHTOA
tan 38° = x9
x = 9 × tan 38°
x = 7.0 cm
SOHCAHTOA
tan 29° = x15
x = 15 × tan 29°
x = 8.3 cm
Label only the two sides you use.
SOHCAHTOA
tan 38° = x9
x = 9 × tan 38°
x = 7.0 cm
SOHCAHTOA
cos 36° = 6x
x = 6 ÷ cos 36°
x = 7.4 cm

Using tangent. Find x to 1 decimal place.

●○○
1

1.4 cm

2

8.0 cm

3

5.6 cm

●●○
1

3.6 cm

2

5.2 cm

3

5.1 cm

●●●
1

4.7 cm

2

10.3 cm

3

4.5 cm

Which ratio? Do not work it out: just decide.

a

CAH

b

SOH

c

TOA

d

SOH

e

TOA

f

CAH

Trigonometry: finding a side worksheet, page 1

Trigonometry: finding a side worksheet, page 2

Answer sheet

  1. You stand 25 m from a tree. The top of the tree is at an angle of 35° above the ground. How tall is the tree?

    17.5 m

  2. A water slide is 40 m long and slopes at 25° to the ground. How high is the top of the slide?

    16.9 m

  3. A zip wire drops 3.4 m from start to end and slopes at 12° to the horizontal. How long is the zip wire?

    3.4 ÷ sin 12° = 16.4 m

  1. Find the length x to 1 decimal place.

    x = 9.2 cm
    x15 cm52°

  2. Find the length x to 1 decimal place.

    x = 6.7 cm
    8 cmx40°

  3. Find the length x to 1 decimal place.

    x = 12.8 cm
    6 cmx28°
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