GCSE OCR Maths 3D trigonometry: The diagram shows a right-angled

The diagram shows a right-angled triangular prism ABCDEF - OCR - GCSE Maths - Question 20 - 2018 - Paper 4

Question 20

The diagram shows a right-angled triangular prism ABCDEF. Calculate angle AFB.

Worked Solution & Example Answer:The diagram shows a right-angled triangular prism ABCDEF - OCR - GCSE Maths - Question 20 - 2018 - Paper 4

Step 1

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Answer

To find angle AFB, we will use the sine function in triangle AFB.

We know:

Using the sine function:

$\sin(AFB) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{AB}{AF} = \frac{18}{40}$

Calculating:

$\sin(AFB) = 0.45$

To find angle AFB, we will take the inverse sine:

$AFB = \sin^{-1}(0.45) \approx 26.57^{\circ}$

Thus, angle AFB is approximately 26.57 degrees.

Step 2

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Answer

Alternatively, we can verify using the cosine rule:

Using the formula:

AF^2 = AB^2 + BF^2 - 2 \cdot AB \cdot BF \cdot \cos(AFB)

Here, AF = 40 cm, AB = 18 cm, and BF = 25 cm.

This gives:

40^2 = 18^2 + 25^2 - 2 \cdot 18 \cdot 25 \cdot \cos(AFB)

Calculating:

$1600 = 324 + 625 - 900 \cdot \cos(AFB)$ $1600 = 949 - 900 \cdot \cos(AFB)$ $900 \cdot \cos(AFB) = 949 - 1600$ $\cos(AFB) = \frac{-651}{900}$

Calculating angle AFB gives approximately the same value when you compute the inverse cosine.

This confirms that angle AFB is consistent, thus concluding our solution.