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Quiz

Year 3: Solving any triangle

10 questions with solutions for year 3: the sine and cosine rules, angle bisectors and medians, parallelograms and trapeziums – review problems.

Type the number or choose the right answer. When you finish, click Check answers and see the solutions.

1. In △ABC: b = 5, c = 7, α = 60°. What is a?

2. In △ABC: a − b = 5 cm, c = 7 cm, R = 7√3/3 cm (γ acute). What is a (cm)?

3. In △ABC: BC = 2√6, ∠ABC = 30°, ∠BCA = 45°. How long is the bisector of ∠ABC?

4. The median from A is tₐ = 15 cm, a = 16 cm, c = 11 cm. What is b?

5. A parallelogram has sides 11 cm and 6 cm and an angle of 112°. The shorter diagonal is about:

6. The median AK = 13√2/4 makes a 30° angle with AC, and ∠ACB = 45°. What is BC?

7. The angles of a triangle are in the ratio 3 ÷ 4 : 8. The ratio longest : shortest side is about:

8. a = 5, b = 3, γ = 96°. The side c is about:

9. In △ABC: c = 7 cm and γ = 60°. The circumradius R is:

10. b = 14 cm, c = 26 cm, β = 32°. How many solutions has the problem?