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M-GEO-051-WS01 · Higher only

Use the sine rule

Worked answers · 20 questions

Student worksheet (PDF)All worked solutions (PDF)

Retrieval

  1. R01In triangle ABC, name the side opposite angle B.

    M-GEO-051-WS01-R01

    Answer
    AC
    Worked steps
    1. The side opposite B joins the other two vertices: A and C.

  2. R02Two angles in a triangle are 54° and 63°. Find the third angle.

    M-GEO-051-WS01-R02

    Answer
    63°
    Worked steps
    1. 180 − 54 − 63 = 63°.

  3. R03Round 12.846 to 3 significant figures.

    M-GEO-051-WS01-R03

    Answer
    12.8
    Worked steps
    1. The first three significant digits are 1, 2, 8. The next digit is 4.

  4. R04Calculate sin 40°. Give your answer to 3 decimal places.

    M-GEO-051-WS01-R04

    Answer
    0.643
    Worked steps
    1. Use degree mode: sin 40° = 0.642787...; round to 0.643.

Fluency

  1. F01Calculate AC. Give your answer to 3 significant figures.

    M-GEO-051-WS01-F01

    Angle A:
    38°
    Angle B:
    72°
    BC:
    9 cm
    Answer
    13.9 cm
    Worked steps
    1. AC / sin 72° = 9 / sin 38°.
    2. AC = 9 × sin 72° / sin 38° = 13.90294665... cm.
    3. AC = 13.9 cm (3 s.f.).

  2. F02Calculate AC. Give your answer to 3 significant figures.

    M-GEO-051-WS01-F02

    Angle A:
    52°
    Angle B:
    61°
    BC:
    12 cm
    Answer
    13.3 cm
    Worked steps
    1. AC / sin 61° = 12 / sin 52°.
    2. AC = 12 × sin 61° / sin 52° = 13.31890008... cm.
    3. AC = 13.3 cm (3 s.f.).

  3. F03Calculate AC. Give your answer to 3 significant figures.

    M-GEO-051-WS01-F03

    Angle A:
    44°
    Angle B:
    83°
    BC:
    7 cm
    Answer
    10 cm
    Worked steps
    1. AC / sin 83° = 7 / sin 44°.
    2. AC = 7 × sin 83° / sin 44° = 10.00178412... cm.
    3. AC = 10 cm (3 s.f.).

  4. F04Calculate AC. Give your answer to 3 significant figures.

    M-GEO-051-WS01-F04

    Angle A:
    31°
    Angle B:
    96°
    BC:
    11 cm
    Answer
    21.2 cm
    Worked steps
    1. AC / sin 96° = 11 / sin 31°.
    2. AC = 11 × sin 96° / sin 31° = 21.24064488... cm.
    3. AC = 21.2 cm (3 s.f.).

Develop

  1. D01Angle B is acute. Calculate B to 1 decimal place.

    M-GEO-051-WS01-D01

    Angle A:
    32°
    Angle B:
    B
    BC:
    8 cm
    AC:
    11 cm
    Answer
    46.8°
    Worked steps
    1. sin B / 11 = sin 32° / 8.
    2. sin B = 11 × sin 32° / 8.
    3. Inverse sine gives 46.77241667...°.
    4. B = 46.8°.

  2. D02Angle B is obtuse. Calculate B to 1 decimal place.

    M-GEO-051-WS01-D02

    Angle A:
    32°
    Angle B:
    B
    BC:
    8 cm
    AC:
    11 cm
    Answer
    133.2°
    Worked steps
    1. sin B / 11 = sin 32° / 8.
    2. sin B = 11 × sin 32° / 8.
    3. Inverse sine gives 46.77241667...°. B is obtuse, so B = 180° − 46.77241667...°.
    4. B = 133.2°.

Apply

  1. A01aThree checkpoints form triangle ABC. AB = 150 m, angle BAC = 62° and angle ABC = 49°. Calculate angle ACB.

    M-GEO-051-WS01-A01a

    Angle A:
    62°
    Angle B:
    49°
    AB:
    150 m
    Answer
    69°
    Worked steps
    1. C = 180° − 62° − 49° = 69°.

  2. A01bCalculate the direct distance AC. Give your answer to 3 significant figures.

    M-GEO-051-WS01-A01b

    Answer
    121 m
    Worked steps
    1. AC / sin 49° = 150 / sin 69°.
    2. AC = 150 × sin 49° / sin 69° = 121.26050828... m.
    3. AC = 121 m (3 s.f.).

Independent practice

Shadow practice

  1. H01Calculate AC. Give your answer to 3 significant figures.

    M-GEO-051-WS01-H01

    Angle A:
    41°
    Angle B:
    66°
    BC:
    8 cm
    Answer
    11.1 cm
    Worked steps
    1. AC / sin 66° = 8 / sin 41°.
    2. AC = 8 × sin 66° / sin 41° = 11.13979587... cm.
    3. AC = 11.1 cm (3 s.f.).

  2. H02Calculate AC. Give your answer to 3 significant figures.

    M-GEO-051-WS01-H02

    Angle A:
    57°
    Angle B:
    74°
    BC:
    10 cm
    Answer
    11.5 cm
    Worked steps
    1. AC / sin 74° = 10 / sin 57°.
    2. AC = 10 × sin 74° / sin 57° = 11.46173161... cm.
    3. AC = 11.5 cm (3 s.f.).

  3. H03Angle B is acute. Calculate B to 1 decimal place.

    M-GEO-051-WS01-H03

    Angle A:
    28°
    Angle B:
    B
    BC:
    6 cm
    AC:
    9 cm
    Answer
    44.8°
    Worked steps
    1. sin B / 9 = sin 28° / 6.
    2. sin B = 9 × sin 28° / 6.
    3. Inverse sine gives 44.76554211...°.
    4. B = 44.8°.

  4. H04Angle B is obtuse. Calculate B to 1 decimal place.

    M-GEO-051-WS01-H04

    Angle A:
    28°
    Angle B:
    B
    BC:
    6 cm
    AC:
    9 cm
    Answer
    135.2°
    Worked steps
    1. sin B / 9 = sin 28° / 6.
    2. sin B = 9 × sin 28° / 6.
    3. Inverse sine gives 44.76554211...°. B is obtuse, so B = 180° − 44.76554211...°.
    4. B = 135.2°.

  5. H05Two angles in a triangle are 37° and 81°. Find the third angle.

    M-GEO-051-WS01-H05

    Answer
    62°
    Worked steps
    1. 180 − 37 − 81 = 62°.

  6. H06Round 0.087463 to 3 significant figures.

    M-GEO-051-WS01-H06

    Answer
    0.0875
    Worked steps
    1. The first significant digit is 8. The fourth significant digit is 6, so round up.

Applied practice

  1. H07A triangular sail has AB = 7 m, angle BAC = 48° and angle ABC = 67°. Calculate the length of edge AC to 3 significant figures.

    M-GEO-051-WS01-H07

    Angle A:
    48°
    Angle B:
    67°
    AB:
    7 m
    Answer
    7.11 m
    Worked steps
    1. Angle C = 180° − 48° − 67° = 65°.
    2. AC / sin 67° = 7 / sin 65°.
    3. AC = 7 × sin 67° / sin 65° = 7.10965311... m.
    4. AC = 7.11 m (3 s.f.).

  2. H08Three survey points form triangle ABC. AB = 180 m, angle BAC = 41° and angle ABC = 73°. Calculate AC to 3 significant figures. Is the direct route AC shorter than 190 m? Justify your answer.

    M-GEO-051-WS01-H08

    Angle A:
    41°
    Angle B:
    73°
    AB:
    180 m
    Answer
    188 m; yes, it is shorter than 190 m.
    Worked steps
    1. Angle C = 180° − 41° − 73° = 66°.
    2. AC / sin 73° = 180 / sin 66°.
    3. AC = 180 × sin 73° / sin 66° = 188.42505825... m.
    4. AC = 188 m (3 s.f.).
    5. The unrounded length 188.42505825... m is below 190 m.