Questions: In the above figure, the radius of curvature is 10 ft and the height of the segment is 2 ft. What's the length of the chord? A. 7.5 ft B. 15 ft C. 10 ft D. 12 ft

In the above figure, the radius of curvature is 10 ft and the height of the segment is 2 ft. What's the length of the chord?
A. 7.5 ft
B. 15 ft
C. 10 ft
D. 12 ft

Transcript text: In the above figure, the radius of curvature is 10 ft and the height of the segment is 2 ft. What's the length of the chord? A. 7.5 ft B. 15 ft C. 10 ft D. 12 ft

Solution

Solution Steps

To find the length of the chord in a circle given the radius and the height of the segment, we can use the formula for the chord length: \( c = 2 \sqrt{r^2 - h^2} \), where \( r \) is the radius and \( h \) is the height of the segment. In this problem, the radius \( r \) is 10 ft and the height \( h \) is 2 ft.

Step 1: Identify the Given Values

We are given the radius of curvature \( r = 10 \, \text{ft} \) and the height of the segment \( h = 2 \, \text{ft} \).

Step 2: Use the Chord Length Formula

The formula to calculate the length of the chord \( c \) in a circle is: \[ c = 2 \sqrt{r^2 - h^2} \]

Step 3: Substitute the Values into the Formula

Substitute \( r = 10 \) and \( h = 2 \) into the formula: \[ c = 2 \sqrt{10^2 - 2^2} = 2 \sqrt{100 - 4} = 2 \sqrt{96} \]

Step 4: Simplify the Expression

Calculate the square root and multiply by 2: \[ c = 2 \times \sqrt{96} \approx 2 \times 9.798 = 19.60 \]