Question

Type the correct answer in the box. Use numerals instead of words.
In the image below, point J is located at the center of the circle, and s is the length of the arc located inside of the triangle.



Given that m∠JKL = 94°, m∠KLJ = 41°, and the radius of the circle is 10 units, find s, rounded to the nearest hundredth.

s = ___
units

Answer 1

The length of the arc located inside the triangle is 7.85 units.

Step-by-step explanation:

The given information are,

• The angle formed at K is 94 degrees.
• The angle formed at L is 41 degrees.

Let us assume,

The angle formed at J be 'x degrees'.

To find the angle J :

The sum of the angles in a triangle measures 180°.

94 + 41 + x = 180

x = 180 - 135

x = 45°

Therefore, the angle formed at J is 45 degree.

To find the length of the arc :

The formula to find length of the arc is given by,

⇒ (central angle / 360) × 2πr

The radius r of the of the circle is 10 units.

⇒ (45 / 360) × 2 × 3.14 × 10

⇒ ( 1/8) × 62.8

⇒ 7.85 units.

The length of the arc located inside the triangle is 7.85 units.