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Consider the diagram shown - HSC - SSCE Mathematics Standard - Question 6 - 2024 - Paper 1

Question 6

Consider the diagram shown. Which of the following is the correct expression for the length of $x$? A. 20 cos 40° B. 20 sin 40° C. $ \frac{20}{\cos 40°} $ D. \( \... show full transcript

Worked Solution & Example Answer:Consider the diagram shown - HSC - SSCE Mathematics Standard - Question 6 - 2024 - Paper 1

Step 1

Identify the triangle and angles

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Answer

We have a triangle where one angle is $40^{\circ}$ and the adjacent side to this angle is of length 20. We need to find the opposite side, labeled as $x$ .

Step 2

Use the sine function

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Answer

To find the length of the opposite side in a right triangle, we can use the sine function, which is defined as:

$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

For our triangle, let ( \theta = 40^{\circ} ). Therefore, we have:

$\sin(40^{\circ}) = \frac{x}{20}$

Step 3

Rearrange the equation to solve for x

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Answer

Rearranging the equation gives us:

$x = 20 \cdot \sin(40^{\circ})$

Step 4

Select the correct answer

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Answer

Thus, the correct expression for the length of $x$ is:

20 sin 40°, which corresponds to option B.

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