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ABCDEF GH is a cuboid - Edexcel - GCSE Maths - Question 20 - 2022 - Paper 2

Question 20

ABCDEF GH is a cuboid. AD = 9cm FD = 13cm Angle GHF = 49°. Work out the size of angle FAH. Give your answer correct to the nearest degree.

Worked Solution & Example Answer:ABCDEF GH is a cuboid - Edexcel - GCSE Maths - Question 20 - 2022 - Paper 2

Step 1

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Answer

In triangle FAH, we know the lengths of AD and FD as well as the angle GHF. We can label the sides accordingly:

Step 2

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Answer

Since we have two sides and the angle between them, we can use the cosine rule to find angle FAH, which can be labeled as θ:

$heta = ext{angle FAH}$

Using the cosine rule: $c^2 = a^2 + b^2 - 2ab imes ext{cos}(C)$ Where:

Calculating side AF:

a = AD = 9, b = FD = 13, C = 49°,

We can substitute these values into the formula.

Step 3

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Answer

After calculating the value of c using the cosine rule, we can find the angle FAH. Alternatively, we can use the sine rule to directly find angle θ:

$\frac{AD}{\sin(49°)} = \frac{FD}{\sin(\theta)}$ (using sine rule)

This can be solved for θ to find angle FAH.

Step 4

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Answer

After performing the calculations, you would find angle FAH, rounded to the nearest degree.

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