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Grade 7 · Higher · free GCSE maths worksheet

Trigonometry with obtuse angles

Edexcel IGCSE

sin (180 - x) = sin x, cos (180 - x) = -cos x and finding both angles.

10 original questions, 30 marks. Type your answers below for an instant mark and a score, or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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How to do it

  1. Obtuse angles share their sine with an acute angle: sin (180° - x) = sin x
  2. Cos and tan flip sign: cos (180° - x) = -cos x and tan (180° - x) = -tan x
  3. sin x = k gives two answers between 0° and 180°: the calculator one and 180° minus it
  4. cos x negative means x is obtuse: the calculator gives the obtuse angle straight away
  5. Sine rule for an angle you are told is obtuse: find the acute angle, then 180° minus it

Watch out: A calculator never gives an obtuse angle from sin⁻¹, so if the angle is obtuse you must subtract the calculator answer from 180°.

Worked example

The angle x is obtuse and sin x = 0.82

Work out the size of angle x. Give your answer correct to 1 decimal place.

sin-1(0.82)=55.08...°

That is the acute angle, but x is obtuse

x=180° - 55.08...°
=124.91...°

x = 124.9°

The questions

1

sin 35° = sin x°, where x is an obtuse angle.

Write down the value of x.

1 mark
Show answer
145
2

Correct to 3 decimal places, sin 40° = 0.643, cos 40° = 0.766 and tan 40° = 0.839

Write down the value of

  1. sin 140°
  2. cos 140°
  3. tan 140°
3 marks
Show answer
a) 0.643 b) -0.766 c) -0.839
3

sin x° = 0.4 and 0 ≤ x ≤ 180

Find both possible values of x. Give your answers correct to 1 decimal place.

  1. the acute value of x
  2. the obtuse value of x
2 marks
Show answer
a) 23.6 b) 156.4
4

In each part, 0 ≤ x ≤ 180

  1. cos x° = −0.5
    Find the value of x.
  2. tan x° = −2.5
    Find the value of x. Give your answer correct to 1 decimal place.
3 marks
Show answer
a) 120 b) 111.8
5

The angle x is obtuse and sin x = 513

Find the exact value of

  1. cos x
  2. tan x
3 marks
Show answer
a) -12/13 b) -5/12
6

In triangle ABC, AB = 9 cm, AC = 6.5 cm and angle BAC = 130°.

Work out the area of triangle ABC. Give your answer correct to 1 decimal place.

2 marks
Show answer
22.4
7

In triangle PQR, PQ = 5 cm, QR = 7 cm and PR = 10.5 cm.

Work out the size of angle PQR. Give your answer correct to 1 decimal place.

3 marks
Show answer
121.2
8

In triangle ABC, AB = 8 cm, BC = 5 cm and angle BAC = 32°.

Angle ACB is obtuse.

Work out the size of angle ACB. Give your answer correct to 1 decimal place.

3 marks
Show answer
122.0
9

In triangle DEF, DE = 11 cm, EF = 7 cm and angle EDF = 25°.

Angle DFE is obtuse.

  1. Work out the size of angle DFE. Give your answer correct to 1 decimal place.
  2. Work out the length of DF. Give your answer correct to 1 decimal place.
5 marks
Show answer
a) 138.4 b) 4.7
10

A triangular field ABC has AB = 120 m and AC = 85 m.

Angle ABC = 38° and angle ACB is obtuse.

Work out the area of the field. Give your answer in m2 correct to 3 significant figures.

5 marks
Show answer
1940

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Every question here is original and written by Robinson Tuition. This topic is on the Pearson Edexcel International GCSE (4MA1) and is not examined on the UK GCSE; the grade is our estimate against the Edexcel grade descriptors. This is not an exam-board paper.

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