Trigonometry: finding an angle

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Walkthrough to print

  1. Find x to 1 decimal place.

    x = 8.4 cm

  2. Find x to 1 decimal place.

    x = 9.6 cm

  3. Find x to 1 decimal place.

    x = 4.1 m

A ramp must not be too steep for a wheelchair. How could you tell how steep a ramp is?

Compare how high it rises with how far along it goes, or measure its angle

Work backwards.

  1. sin 30° = 0.5Which angle has a sine of 0.5?

    30°

  2. cos 60° = 0.5Which angle has a cosine of 0.5?

    60°

  3. tan 45° = 1Which angle has a tangent of 1?

    45°

Casio fx-83GT X calculator
fx-83GT X
Casio fx-83GT CW calculator
fx-83GT CW

SHIFT, then sin, gives sin−1.
It finds the angle.

  1. sin−1(0.8)

    53.1°

  2. cos−1(0.25)

    75.5°

  3. tan−1(3)

    71.6°

To 1 decimal place.

Inverse
The function that undoes another.
sin−1, cos−1, tan−1
The inverses of sin, cos and tan. They give the angle from the ratio.

Finding an angle

  1. Labelthe two sides you know.
  2. PickSOH, CAH or TOA.
  3. Writethe ratio with the numbers in.
  4. Use the inverse:x = sin−1( ), cos−1( ) or tan−1( ).
  5. Calculateand round as asked.
Walkthrough to print

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

x13 cm8.5 cmx10.5 cm6 cmx4.2 cm7.3 cmx16.4 m11 mx10.6 cm9.4 cmx7 cm10 cmx9 m5.5 mx12 mm7.5 mmHOHAOAHAHOOAHAOA
SOHCAHTOA
sin x = 8.513
x = sin−1 8.513
x =40.8°
SOHCAHTOA
cos x = 815
x = cos−1 815
x =57.8°
SOHCAHTOA
sin x = 8.513
x = sin−1 8.513
x =40.8°
SOHCAHTOA
cos x = 6.511
x = cos−1 6.511
x =53.8°
SOHCAHTOA
tan x = 106
x = tan−1 106
x =59.0°
SOHCAHTOA
tan x = 7.510
x = tan−1 7.510
x =36.9°
SOHCAHTOA
tan x = 106
x = tan−1 106
x =59.0°
SOHCAHTOA
tan x = 813
x = tan−1 813
x =31.6°
SOHCAHTOA
sin x = 8.513
x = sin−1 8.513
x =40.8°
SOHCAHTOA
sin x = 811
x = sin−1 811
x =46.7°
SOHCAHTOA
sin x = 8.513
x = sin−1 8.513
x =40.8°
SOHCAHTOA
cos x = 7.510
x = cos−1 7.510
x =41.4°
SOHCAHTOA
tan x = 106
x = tan−1 106
x =59.0°
SOHCAHTOA
tan x = 512
x = tan−1 512
x =22.6°

Find angle x to 1 decimal place.

a

x = 36.2°

b

x = 58.0°

c

x = 67.4°

d

x = 34.7°

Trigonometry: finding an angle worksheet, page 1

Trigonometry: finding an angle worksheet, page 2

Answer sheet

Sketch each one first. Give your answers to 1 decimal place.

  1. A zip wire 80 m long runs from the top of a tower 12 m high down to the ground.
    Find the angle between the wire and the ground.

    8.6°

  2. A rectangle is 8 cm long and 5 cm wide.
    What angle does its diagonal make with the long side?

    32.0°

  3. A roof rafter is 4.5 m long.
    It reaches 3.8 m across from the edge of the roof to below the ridge.
    Find the angle between the rafter and the horizontal.

    32.4°

  1. Find angle x to 1 decimal place.

    x = 27.0°
    5 cm11 cmx

  2. Find angle x to 1 decimal place.

    x = 52.1°
    7 cm9 cmx

  3. A ramp 6 m long rises 0.8 m. Find its angle to the ground to 1 decimal place.

    7.7°
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