Dr. J's Maths.com
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Trigonometry - Sine rule.
Test Yourself 1 - Solutions.


 

The questions based on the Sine Rule below relate to:
1. The marking of a triangle.
2. Finding the length of a side.
3. Finding the size of an angle.
4. Applied questions.

 

Marking up the triangle.

1.

Side C has no opposite angle.

2.

Angle c has no opposite side.
Basic - find the length of a side
(answer to 2 dps).		 3. 4.
  5. 6.
  7. 8.
Side not opposite 9. 10.
  11.

12.

 

13.

14. (i)

(ii)

 

15.

(i) To find BC we need the angle at C:

(ii) We also need the length AC:

16.

The triangle does not have two pairs of matching sides and angles. Hence the 3rd angle (at E) must be calculated:

E = 180 - 56 - 48 = 76.

(i)

(ii)

Basic - find the size of an angle. 17. 18.
  19. 20.
  21. 22.
Angle not opposite 23. By drawing arrows/butterfly wings, we note the side opposite the required angle has no length indicated. Hence we must first find the size of
∠ LNM.

24.

Drawing our usual arrows to link the angles to the side opposite shows side whose length we do not know. So draw the green arrow from the third angle to the other given side and calculate the size of the angle for that arrow. Then use angle sum of a triangle:
The Ambiguous Case. 25. 26.
  27. 28.
  29. (i)

(ii)

 

30. (i)

(ii)

Applied 31.

Obtuse angle - 180° - 25°- 40° = 115°
 

32. (i)

(ii)

(iii)

  33. (i)

Note need to find the angle α before calculating the angle β.

 (ii)