Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
![**Triangle Problem: Find the Length of the Side**
In the given right-angled triangle, we are tasked with finding the length of side \( x \).
**Diagram Description:**
- The triangle is a right-angled triangle.
- The hypotenuse of the triangle is labeled as 12 units.
- One of the angles in the triangle is \( 42^\circ \), situated adjacent to side \( x \).
**Question:**
2. Find \( x \).
**Multiple Choice Answers:**
- A. 10.4
- B. 8.0
- C. 8.9
- D. 10.8
To solve for \( x \), one would typically use trigonometric functions such as sine, cosine, or tangent. Given the angle and the hypotenuse, using the cosine function would be appropriate since it relates the adjacent side (which is \( x \)) to the hypotenuse.
\[ \cos(42^\circ) = \frac{x}{12} \]
By rearranging to solve for \( x \):
\[ x = 12 \times \cos(42^\circ) \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6756c5c2-608f-4015-b13f-deb910f8c3e1%2Ffcb0bb0f-ad34-4c61-8c13-95590c2f6d6a%2Ft0fsc7h_processed.jpeg&w=3840&q=75)
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