Hint
Use the stated units and precision. Apply Pythagoras within the horizontal base first.
Worked solution
(a)
Apply Pythagoras within the horizontal base first.
The horizontal projection has length \(\displaystyle \sqrt{9+16}=5 \mathrm{cm}\).
Answer: \(5\)
(b)
Use the base diagonal and perpendicular height as legs of a second right triangle.
The projection and vertical height give \(\sqrt{41}\), rounding to \(6.40\) cm.
Answer: \(6.40\)
(c)
Use the angle between the line and its horizontal projection.
The angle has tan θ=height/base-diagonal=\(\displaystyle \frac{4}{5}\), giving \(38.7\)°.
Answer: \(38.7\)
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 Pythagoras within the horizontal base first.
- 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 base diagonal and perpendicular height as legs of a second right triangle.
- 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 angle between the line and its horizontal projection.
- 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.