GCSE OCR Maths Angle Facts: Here is a right-angled triangle.

Here is a right-angled triangle - OCR - GCSE Maths - Question 16 - 2020 - Paper 3

Question 16

Here is a right-angled triangle. Use trigonometry to work out the value of x. x = ...................................................... 8 cm 34° Not to scale

Worked Solution & Example Answer:Here is a right-angled triangle - OCR - GCSE Maths - Question 16 - 2020 - Paper 3

Step 1

Use trigonometry to work out the value of x.

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Answer

In a right-angled triangle, we use trigonometric ratios. Here, we have:

Opposite side = 8 cm
Angle = 34°

To find the adjacent side (x), we can use the tangent function:

$an(34^{ ext{o}}) = \frac{\text{opposite}}{\text{adjacent}}$

Substituting the values:

$\tan(34^{ ext{o}}) = \frac{8}{x}$

Rearranging gives:

$x = \frac{8}{\tan(34^{\text{o}})}$

Now calculating:

Use a calculator to find ( \tan(34^{\text{o}}) ).
Compute:

$x = \frac{8}{0.6745} \approx 11.85 \text{ cm}$

Thus, the value of x is approximately 11.85 cm.

Step 2

Work out the size of the exterior angle of a regular 12-sided polygon.

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Answer

To find the exterior angle of a regular polygon, we use the formula:

$\text{Exterior Angle} = \frac{360^{\text{o}}}{n}$

where ( n ) is the number of sides. For a 12-sided polygon:

$\text{Exterior Angle} = \frac{360^{\text{o}}}{12} = 30^{\text{o}}$

Therefore, the size of the exterior angle of a regular 12-sided polygon is 30°.

Here is a right-angled triangle - OCR - GCSE Maths - Question 16 - 2020 - Paper 3

Worked Solution & Example Answer:Here is a right-angled triangle - OCR - GCSE Maths - Question 16 - 2020 - Paper 3

Use trigonometry to work out the value of x.

Work out the size of the exterior angle of a regular 12-sided polygon.

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