Hint
Use the stated units and precision. Apply the sine rule and inverse sine in degree mode.
Worked solution
(a)
Apply the sine rule and inverse sine in degree mode.
The sine rule gives \(\displaystyle \sin B=\)\(\displaystyle \frac{6 \sin{\left(\frac{7 \pi}{36} \right)}}{5}\). The acute solution rounds to \(43.5\)°.
Answer: \(43.5\)
(b)
Use the second sine solution and test the triangle angle sum.
The supplementary candidate 180°−B rounds to \(136.5\)° and leaves a positive third angle.
Answer: \(136.5\)
(c)
Use the acute-angle branch in the triangle sum before rounding.
Subtract A and the unrounded acute B from 180° to obtain \(101.5\)°.
Answer: \(101.5\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 2 marks
- 1 mark: Apply the sine rule and inverse sine in degree mode.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Use the second sine solution and test the triangle angle sum.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Use the acute-angle branch in the triangle sum before rounding.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 6 marks.