Paper 22 Q17IGCSE 0580 May/June 2023

Question

17 NOT TO 92.5 cm SCALE x° 71 cm The diagram shows a triangle with an acute angle marked x°. The area of the triangle is 2143cm^{2}. Work out the value of x.

Diagram: # Diagram Description for Question 17 **Diagram type:** Triangle with one acute angle marked **Key measurements/labels:** - Two sides labeled: 92.5 cm and 71 cm - Angle between these sides: x° - Area of triangle: 2143 cm² **Key relationships:** - "NOT TO SCALE" notation present - The angle x° is acute and appears to be formed between the two given sides

This question tests your ability to use the sine rule for finding angles when you know two sides and the area of a triangle. This is a key skill for solving real-world problems involving triangles where direct angle measurement isn't possible.

Step-by-Step Solution

Key Takeaway

When you know two sides of a triangle and its area, use Area = (1/2)ab sin(C) to find the included angle.

Common Mistakes

Using the wrong area formula - students might try to use (1/2) × base × height instead of the sine formula when the angle is given
Calculator in radians mode - this would give an incorrect final answer as the question requires degrees

Exam Tip

Always check your calculator is in degree mode when working with angles, and verify your answer makes sense - acute angles are less than 90°.

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