Missing sides with sine and cosine rules, and triangle areas.
Example 1
In triangle ABC, A=56∘,B=38∘ and side a=13cm. Find side b in cm. Give your answer to 2 decimal places.
Sine ruleDiagram not to scaleShow worked answer
Answer: 9.65
- Use the sine rule: sinBb=sinAa.
- b=sin(56∘)13sin(38∘).
- Rounded answer: 9.65.
Example 2
Two sides of a triangle are 10cm and 9cm with included angle 110∘. Find the opposite side in cm. Give your answer to 2 decimal places.
Cosine ruleDiagram not to scaleShow worked answer
Answer: 15.57
- Use c2=a2+b2−2ab cosC.
- c2=102+92−2(10)(9)cos(110∘).
- Take the positive square root.
- Rounded answer: 15.57.
Example 3
Two sides of a triangle are 6cm and 10cm with included angle 30∘. Find its area in cm2.
Triangle areaDiagram not to scaleShow worked answer
Answer: 15
- Area = ½ab sinC.
- Area = ½ ×6×10× ½ =15cm2.