https://file.aiquickdraw.com/mathbot/file/172737068434581a93xpl.jpg

The image you've uploaded depicts a right-angled triangle with sides of 33 cm, 37 cm, and 17 cm. The angle in question is \(63^\circ\), and the problem is asking to express \(\cos 63^\circ\) as a fraction.

From the triangle's description:
- The hypotenuse (the side opposite the right angle) is 37 cm.
- The adjacent side (next to the \(63^\circ\) angle) is 33 cm.

The cosine of an angle in a right-angled triangle is defined as the length of the adjacent side divided by the length of the hypotenuse. Therefore, for \( \cos 63^\circ \):
\[
\cos 63^\circ = \frac{\text{adjacent side}}{\text{hypotenuse}} = \frac{33}{37}
\]

Expressed as a fraction, \(\cos 63^\circ = \frac{33}{37}\).

Would you like to know more about this or any other math-related topic? Here are some additional questions to consider:

1. How can you verify the accuracy of the trigonometric values provided?
2. What is the sine of the \(63^\circ\) angle in the same triangle?
3. How would you find the tangent of \(63^\circ\) using the same triangle?
4. Could you calculate the angles and sides of different triangles if other sides were known?
5. What are the real-world applications of cosine in a triangle?

Tip: Always ensure your triangle's side lengths and angles are consistent with the Pythagorean theorem, especially in theoretical or classroom settings.

Using the right-angled triangle below, write cos 63° as a fraction.

Learn how to calculate cos(63°) using a right-angled triangle. The adjacent side is 33 cm, and the hypotenuse is 37 cm, resulting in cos(63°) = 33/37. This example is ideal for students in Grades 8-10 studying trigonometric ratios.

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