4024/21 Oct/Nov 2021, Question 6: Choosing the Right Trigonometric Ratio

Part (ai) · 3 marks

Using Pythagoras on the sides 2x, 8 and 3x + 5, show the result 5x² + 30x − 39 = 0.

1. 18² + (2x)² = (3x + 5)²
2. 264 + 4x² = 9x² + 15x + 15x + 25
3. 30 = 5x² + 30x − 39, so 5x² + 30x − 39 = 0

Answer8² + (2x)² = (3x + 5)², 64 + 4x² = 9x² + 15x + 15x + 25 leading to 5x² + 30x − 39 = 0

Part (aii) · 3 marks

Find the roots of 5x² + 30x − 39 = 0, showing working, rounded to 2 decimal places.

1. 1x = (−30 ± √(30² − 4 × 5 × (−39)))/(2 × 5)
2. 2= (−30 ± √1680)/10
3. 3x = 1.098… ≈ 1.10 or x = −7.098… ≈ −7.10

Answer1.10 and −7.10

Part (aiii) · 2 marks

Work out the area of the triangle in cm².

1. 1From part (ii), x = 1.0987… (positive root of 5x² + 30x − 39 = 0)
2. 2Vertical side = 2x = 2.197… cm
3. 3Area = 1/2 × 8 × 2.197… = 8.79 cm², so 8.78 to 8.80

Answer8.78 to 8.80

Part (b) · 4 marks

In triangle ABC with a right angle at A, hypotenuse 12 cm and angle ACB 35°, work out the shortest distance from A to BC.

1. 1AC = 12 cos 35 = 9.829…
2. 2Shortest distance = perpendicular from A to BC = AC × sin 35
3. 3= 9.829… × sin 35 = 5.638… ≈ 5.64 cm

Answer5.63 to 5.64

More past-paper questions on choosing the right trigonometric ratio

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