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Here is a right-angled triangle - OCR - GCSE Maths - Question 23 - 2021 - Paper 1

Question 23

Here is a right-angled triangle. Work out the value of $h$. ![Triangle](https://example.com/triangle-image.png) Here is a right-angled triangle with one angle me... show full transcript

Worked Solution & Example Answer:Here is a right-angled triangle - OCR - GCSE Maths - Question 23 - 2021 - Paper 1

Step 1

Use Trigonometric Ratios

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Answer

In the right-angled triangle, we use the cosine function because we know the adjacent side and the angle. The cosine of an angle in a right triangle is given by:

$\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$

Here, the adjacent side is $h$ cm, the hypotenuse is 8 cm, and the angle $\theta$ is 60°.

Step 2

Set Up the Equation

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Answer

Using the cosine function, we set up the equation as follows:

$\cos(60°) = \frac{h}{8}$

Knowing that $\cos(60°) = 0.5$ , we can substitute this value into the equation.

Step 3

Solve for $h$

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Answer

Substituting the value of $\cos(60°)$ into the equation gives:

$0.5 = \frac{h}{8}$

To find $h$ , we multiply both sides by 8:

$h = 8 \times 0.5 = 4$

Thus, the value of $h$ is 4 cm.

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