Coordinates and trigonometry · Ages 14–15
Finding a side worksheet
Part of: Trigonometry
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Finding a side worksheet
Coordinates and trigonometry · Ages 14–15
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.The right-angled triangle in the picture has a hypotenuse of 13 cm, and the angle marked is 73°. Correct to 1 decimal place, what is x, in cm?
Answer:
2.The right-angled triangle in the picture has a hypotenuse of 5 cm, and the angle marked is 53°. Correct to 1 decimal place, what is x, in cm?
Answer:
3.The right-angled triangle in the picture has a hypotenuse of 25 cm, and the angle marked is 76°. Correct to 1 decimal place, what is x, in cm?
Answer:
4.In the right-angled triangle in the picture the angle marked is 75°, and the side opposite it is 22 cm. Correct to 1 decimal place, what is the hypotenuse x, in cm?
Answer:
5.In the right-angled triangle in the picture the angle marked is 34°, and the side beside it is 21 cm. Correct to 1 decimal place, what is x, in cm?
Answer:
6.In the right-angled triangle in the picture the angle marked is 39°, and the side beside it is 30 cm. Correct to 1 decimal place, what is x, in cm?
Answer:
7.In the right-angled triangle in the picture the angle marked is 55°, and the side opposite it is 19 cm. Correct to 1 decimal place, what is the hypotenuse x, in cm?
Answer:
8.The right-angled triangle in the picture has a hypotenuse of 21 cm, and the angle marked is 39°. Correct to 1 decimal place, x = cm, and the triangle's area = cm² (from the sides before rounding).
Fill in each blank
Answer:
9.In the right-angled triangle in the picture the angle marked is 68°, and the side opposite it is 7 cm. Correct to 1 decimal place, what is x, in cm?
Answer:
10.The right-angled triangle in the picture has a hypotenuse of 24 cm, and the angle marked is 32°. Correct to 1 decimal place, x = cm, and the triangle's area = cm² (from the sides before rounding).
Fill in each blank
Answer:
Part B: Choose, or true or false (2 marks each)
11.The right-angled triangle in the picture has a hypotenuse of 5 cm, and the angle marked is 66°. Which working finds x?
- A. x = 5 × sin 66°
- B. x = 5 × tan 66°
- C. x = 5 × cos 66°
- D. x = 5 ÷ sin 66°
Choose the right answer
Answer:
12.The right-angled triangle in the picture has a hypotenuse of 23 cm, and the angle marked is 14°. Correct to 1 decimal place, x = 22.3 cm.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.A ramp inclined at 3° is 20 m long, measured along it. Correct to 1 decimal place: it rises m over m across.
Fill in each blank
Working:
Answer:
14.A ladder 10 m long leans on a wall at 67° to the ground. Correct to 1 decimal place, how high up the wall does it reach, in m?
Working:
Answer:
15.Fong flies a kite on 45 m of string, pulled straight at 51° to the horizontal, her hand 1.5 m above the ground. Correct to 1 decimal place, how high is the kite, in m?
Working:
Answer:
16.A slide's top is 7 m above the ground and the slide makes 51° with the ground. Find its length (to 1 decimal place): put the steps in order.
- A. Length = 7 ÷ sin 51°
- B. sin 51° = 7 ÷ length
- C. Length = 7 ÷ 0.7771 ≈ 9 m
Write the letters in the right order
Working:
Answer:
17.A ramp inclined at 11° is 13 m long, measured along it. Correct to 1 decimal place: it rises m over m across.
Fill in each blank
Working:
Answer:
18.Fong flies a kite on 45 m of string, pulled straight at 69° to the horizontal, her hand 1.4 m above the ground. Correct to 1 decimal place, how high is the kite, in m?
Working:
Answer:
Show the answers and working
Finding a side worksheet: Answers and working
Part A: Working out and filling in
1. 3.8 cm
x is beside the 73° angle: cos 73° = x13, so x = 13 × cos 73° ≈ 3.8 cm.
2. 4 cm
x is opposite the 53° angle, the hypotenuse known: sin 53° = x5, so x = 5 × sin 53° ≈ 4 cm.
3. 24.3 cm
x is opposite the 76° angle, the hypotenuse known: sin 76° = x25, so x = 25 × sin 76° ≈ 24.3 cm.
4. 22.8 cm
sin 75° = 22x: x is underneath, so divide: x = 22 ÷ sin 75° ≈ 22.8 cm.
5. 14.2 cm
x is opposite and 21 adjacent: tan 34° = x21, so x = 21 × tan 34° ≈ 14.2 cm.
6. 24.3 cm
x is opposite and 30 adjacent: tan 39° = x30, so x = 30 × tan 39° ≈ 24.3 cm.
7. 23.2 cm
sin 55° = 19x: x is underneath, so divide: x = 19 ÷ sin 55° ≈ 23.2 cm.
8. 16.3, 107.8
x = 21 cos 39° ≈ 16.3; the other short side is 21 sin 39°; area = 12 × 21 cos 39° × 21 sin 39° ≈ 107.8 cm².
9. 2.8 cm
x is the adjacent side: tan 68° = 7x, so x = 7 ÷ tan 68° ≈ 2.8 cm. Or by the other acute angle: x = 7 × tan(90° − 68°).
10. 20.4, 129.4
x = 24 cos 32° ≈ 20.4; the other short side is 24 sin 32°; area = 12 × 24 cos 32° × 24 sin 32° ≈ 129.4 cm².
Part B: Choose, or true or false
11. A. x = 5 × sin 66°
sin 66° = opposite ÷ hypotenuse = x5, so x = 5 × sin 66°.
12. False
x is the opposite side: 23 × sin 14° ≈ 5.6 cm; cos gives the adjacent side.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 1, 20
The length along the ramp is the hypotenuse: the rise is 20 sin 3° ≈ 1, across 20 cos 3° ≈ 20.
14. 9.2 m
The ladder is the hypotenuse and the height opposite the 67° angle: 10 × sin 67° ≈ 9.2 m.
15. 36.5 m
The kite is 45 × sin 51° above her hand, plus the hand's 1.5: about 36.5 m (rounded at the end).
16. B → A → C
The slide is the hypotenuse, the height opposite: sin 51° = 7length, so length = 7 ÷ sin 51° ≈ 9 m.
17. 2.5, 12.8
The length along the ramp is the hypotenuse: the rise is 13 sin 11° ≈ 2.5, across 13 cos 11° ≈ 12.8.
18. 43.4 m
The kite is 45 × sin 69° above her hand, plus the hand's 1.4: about 43.4 m (rounded at the end).
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