Find the length of a chord which subtends an angle of 58 degrees at the center of a circle with radius 16 cm.

Answer 1

To find the length of the chord, we can use the formula:

\[ \text{Length of chord} = 2r \sin \left(\frac{\theta}{2}\right) \]

where r is the radius of the circle and θ is the angle subtended by the chord at the center.

Plugging in the values r = 16 cm and θ = 58 degrees:

\[ \text{Length of chord} = 2(16) \sin \left(\frac{58}{2}\right) \]
\[ \text{Length of chord} = 32 \sin(29) \]

Using a calculator, we find that \( \sin(29) \approx 0.4848 \):

\[ \text{Length of chord} \approx 32 \times 0.4848 \]
\[ \text{Length of chord} \approx 15.515 \, \text{cm} \]

Therefore, the length of the chord which subtends an angle of 58 degrees at the center of a circle with radius 16 cm is approximately 15.52 cm.