Trigonometry: missing sides and angles, mixed

The Maths Habit Handout to print

Find the angle x to 1 decimal place.

a

26.4°

b

41.4°

c

67.4°

A ski slope drops 120 m.
What else would you need to know to say how steep it is?

Side or angle? Which ratio? Just decide.

a

Side, SOH

b

Angle, CAH

c

Side, TOA

d

Angle, TOA

e

Side, CAH

f

Angle, SOH

Finding a side

Finding an angle

1

Label only the two sides you use (O, A, H from the angle).

Label the two sides you know.

2

Pick SOH, CAH or TOA.

Pick SOH, CAH or TOA.

3

Write the ratio with the numbers in.

Write the ratio with the numbers in.

4

Rearrange: x on top, multiply; x on the bottom, divide.

Use the inverse: θ = sin−1( ), cos−1( ) or tan−1( ).

5

Calculate round as asked.

Calculate round as asked.

Label the two sides you use with O, A or H.

38°14 cmxx10.5 cm6 cmx4.6 cm8 cm47°x9 cm62°x11.5 mx12 cm9.8 cmx6.5 m5.1 m44°x7.2 cmHOHAOAOAHOHAOAHA
Label only the two sides you use.
SOHCAHTOA
cos 33° = 7x
x = 7 ÷ cos 33°
x = 8.3 cm
SOHCAHTOA
tan x = 69
x = tan−1(6 ÷ 9)
x = 33.7°
Label the two sides you know.
SOHCAHTOA
cos x = 4.57.5
x = cos−1(4.5 ÷ 7.5)
x = 53.1°
SOHCAHTOA
sin 52° = x9
x = 9 × sin 52°
x = 7.1 cm
Label the two sides you know.
SOHCAHTOA
cos x = 4.57.5
x = cos−1(4.5 ÷ 7.5)
x = 53.1°
SOHCAHTOA
tan 38° = 6x
x = 6 ÷ tan 38°
x = 7.7 cm
Label the two sides you know.
SOHCAHTOA
cos x = 4.57.5
x = cos−1(4.5 ÷ 7.5)
x = 53.1°
SOHCAHTOA
sin x = 511
x = sin−1(5 ÷ 11)
x = 27.0°
Label the two sides you know.
SOHCAHTOA
cos x = 4.57.5
x = cos−1(4.5 ÷ 7.5)
x = 53.1°
SOHCAHTOA
cos 64° = x12
x = 12 × cos 64°
x = 5.3 cm

Find x to 1 decimal place.

a

6.9 cm

b

35.7°

c

3.9 cm

d

46.2°

e

13.0 cm

f

54.0°

Trigonometry: missing sides and angles, mixed worksheet, page 1

Trigonometry: missing sides and angles, mixed worksheet, page 2

Extension: odd ones out. Find x in each triangle and cross off its answer. Two answers are left over. What mistake gives each one?

a

7.5 cm

b

24.6°

c

3.5 cm

d

54.8°

54.8°8.6 cm24.6°3.5 cm65.4°7.5 cm

8.6 cm: 8 ÷ tan 43° in a, dividing when x is on top

65.4°: the other angle in b, not the one marked x

Answer sheet

Sketch it first. Is it a side or an angle?

  1. A ferry sails from a port on a bearing of 115° for 14 km. How far south of the port is it now? Give your answer to 1 decimal place.

    5.9 km

  2. A ski run is 850 m long and drops 120 m from top to bottom. Find the angle the run makes with the horizontal. Give your answer to 1 decimal place.

    8.1°

  3. You stand on level ground 75 m from the foot of a wind turbine. The angle up from the ground to its hub is 43°. How high is the hub? Give your answer to 1 decimal place.

    69.9 m

  1. Find the length x to 1 decimal place.

    x = 9.5 cm
    x14 cm47°

  2. Find the angle x to 1 decimal place.

    x = 36.0°
    11 cm8 cmx

  3. A 2.6 m rope runs from the top of an upright pole to a peg 1.8 m from its foot. Find its angle to the ground.

    Angle = 46.2°
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