Question

Determine the length of a chord whose central angle is 75° in a circle with a radius of 12 inches.

Answer 1

Answer:

Step-by-step explanation:

length=sqare root of(12^2+12^2-2*12*12*cos(75))=14.6

Answer 2

The length of a chord whose central angle is 75° in a circle with a radius of 12 inches is 14.6 inches.

What is a circle?

A circle is the set of all points in the plane that are a fixed distance (the radius) from a fixed point (the center)

What is central angle of a circle?

A central angle is an angle with endpoints and located on a circle's circumference and vertex located at the circle's center

How to find the length of the chord?

• Here, the radius and the chord forms a triangle, whose vertical angle is 75°.

• We know that for a triangle ABC , we can easily write,

$cos A = \frac{b^{2}+c^{2}-a^{2}}{2bc}$, where a, b ,c are the sides opposite to ∠A, ∠B, ∠C respectively.

In triangle, let ∠A = 75°.

∴ We can write, $cos 75 = \frac{b^{2}+c^{2}-a^{2}}{2bc}$.

• Here b and c are actually the radius of the circle which is 12 inches.
• a is actually the chord of the circle.
• We actually need to find the value of a.

So,  we can write,

(cos 75)(2 x 12 x 12) = (12)² + (12)² - a²

⇒ a = 14.6

∴ the length of the chord is 14.6 inches.

Find more about "Circles" here : https://brainly.com/question/24375372

#SPJ2