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The diagram shows a triangular field PQR which is used to grow organic carrots - OCR - GCSE Maths - Question 18 - 2020 - Paper 1
Question 18
The diagram shows a triangular field PQR which is used to grow organic carrots. PQ = 100 m, PR = 80 m and angle RPQ = 30°. In recent years, an average of 2.5 kg of... show full transcript
Worked Solution & Example Answer:The diagram shows a triangular field PQR which is used to grow organic carrots - OCR - GCSE Maths - Question 18 - 2020 - Paper 1
Step 1
Calculate the Area of Triangle PQR
Answer
To find the area of triangle PQR, we can use the formula:
ext{Area} = rac{1}{2} imes ext{base} imes ext{height}However, since we have two sides and the angle between them, we can use:
ext{Area} = rac{1}{2} imes a imes b imes ext{sin}(C)Where:
- a = PQ = 100 m
- b = PR = 80 m
- C = angle RPQ = 30°
This gives us:
ext{Area} = rac{1}{2} imes 100 imes 80 imes ext{sin}(30°) \ = rac{1}{2} imes 100 imes 80 imes rac{1}{2} \ = rac{1}{2} imes 100 imes 40 \ = 2000 ext{ m}^2Step 2
Step 3
Why might the answer to part (a) be unreliable?
Answer
The answer to part (a) might be unreliable due to various factors such as:
- Variability in crop yield: Depending on weather conditions, soil quality, and other environmental factors, the actual yield of carrots can vary significantly from the average.
- Changes in harvesting practices: If more or fewer carrots were harvested than in previous years, this could affect the total mass.
- Errors in measurements: If the dimensions of the field or the yield per square metre were inaccurately measured, this could lead to incorrect calculations.